Your order has a couple of very useful options to their disposal. Any adventurer with minimal siege experience would agree. This isn't the stuff of tactical geniuses.
1) First you'll clear the forest around the monastery. Regardless of your ranged weaponry you want a clear line of sight. In the very least to prevent the enemy from sneaking up on the compound. So clear the forest, stockpile the wood inside for other projects.
2) Dig a moat. No need to fill it, just dig a deep moat and on the inside create a wall of wooden stakes. Preferably put some stakes in a more forward position. This forces the attackers to either work their way through the stakes in the open or use the designated entrance where the defenders can concentrate their defenses.
3) For weapons your order will mainly make two weapons, maces and spears. Spears were probably till the invention of the gun the most deadly weapon in all of history, maybe even up till the first automatic weapon. Spears are easy to use, cheap to make and create distance between you and whatever wants to hurt you.
Philip of Macedon trained his men into a phalanx in a single winter. Drilling with spears isn't that hard and I feel if you adventurer has seen some form of phalanx or hoplite warfare before he could drill them.
Your second main weapon will be a mace. Bronze headed maces are easy to make and even easier to use. There is a reason they existed well into the middle ages. Bronze is denser then steel. That makes a bronze mace head heavier then a steel one of similar size.
Maces have another advantage over swords and axes. They don't need edge alignment. A mace head doesn't have a cutting edge. The mace doesn't really care with what aligned you hit your target. Edge alignment is a skill, a skill I doubt your order has the time to master. Be smart and stick with maces and spears.
4) Touch them from afar. Your order should try and get their hands on ranged weaponry with all their might. Having them in combination with a wall is a huge force multiplier. They should have some hunting bows I imagine. They live next to a forest after all.
Making more bows will be difficult. Bow making is an art, one that takes a long while to master. Not only that but good bow wood takes months to dry before it can be worked with. Simply put, they don't have the time to dry the material and practice. Unless we're talking years before the enemy shows up.
What they can make and train with are javelins and slings. Javelins don't require fletching and you're stocked up on wood from clearing the area around the compound. Metal tips is optional, unless your enemy is fully clad in mail wooden tips will hurt.
That brings us to slings. Slings are amazing, easy to make and easy to learn to use. They don't require exceptional physical strength unlike a longbow. Ammo will be plentiful, small stones, a finger shaped mold with lead for increased penetration.
This is an excellent video on the ease of use and lethality of slings.
Armed with slings from the walls your order could rain down death upon your enemies far before they reached the moat/ditch and the stakes. Accuracy isn't paramount in a volley, just launch at the blob of enemies with a few dozen men.
Note on crossbows, crossbows can be complex metal instruments of death but they don't need to. Crossbows go back as far as at least 500BC. As far back as 400BC they were a staple of the Chinese military. They became particularly popular in Europe around 500AD when Germanic migrators moved through Europe. They carried crossbows for hunting purposes, not warfare. A simple Greek crossbow from antiquity:
They're actually great tools for hunting, far easier to shoot then a bow. And animals don't wear armor. There is no need for a hard to span crossbow when you hunt deer. The animal is relatively close by and a soft target. I really think your order will have a nice collection of hunting crossbows.
Regardless, crossbows aren't easier to make then regular bows. They still require the bow part which takes to long to make so no additional crossbows will be available.
There several other preparations your order then undertake but I'm not 100% sure how certain your adventurer would know them. Stock up on water and cover any easily flammable roofs like reed. Fire arrows had a huge and lighting roofs on fire was one.
Create covers for the windows so you can lean out while being shielded from the sides and top. Keep the bottom open so you can throw stuff at the enemy.
Sketch:
A, Moat with stakes. Horizontal one is buried at ground level. Keep them apart enough that it won't function as cover. But not so far apart the enemy can easily carry ladders or move in a shield wall or testudo like formation.
B, I assume the walls are more a thick outer wall of some of the buildings then a true fortified wall that can be patrolled. You'll need to build wooden fortifications instead. This was actually quite common. A lot of walls had a row of holes near the top one could fit a thick beam in. On top of this row of beams one could build wooden fortifications.
They would need to be build in such a way that the bottom has a hole to attack the besiegers with. This can simply be throwing down heavy rocks but also boiling pitch, arrows, bolts and javelins.
C1, variation if your wall lacks any system to put in beams you might want to build over the interior buildings. This is also a good idea if the roofs are vulnerable to fire. Planks covered in soaked hide is much harder to ignite.
C2, Topview of the above.
D, it could even create an interior walkway. Might protect the ground from projectiles as well.
E, an experienced defender would insist on two ditches. An outer one with stakes to slow down the attackers without providing cover and a second inner one. The inner one would have a wooden bridge at the gate(s) that can easily be destroyed, denying it's use to the enemy. That second ditch should also be filled with some stakes if only to prevent the enemy from charging the walls directly.
F1, exterior ditch with the stake setup of A. Earth should be placed inside to create a minor earthen wall to secure the stakes in.
F2, interior ditch with simple vertical stakes. Can be shallower then the exterior ditch.
F3, outer wall of the compound. As I picture it inside there is a collection of buildings. Their outer walls are reinforced and connected, creating a compound. From the top left clockwise:
Entrance and lodgings for travelers, workshops, tower with sundial and messaging system like a bell, storage, (vegetable) garden, waste disposal/latrine, storage, sleeping quarters, mess hall, inside the main temple can be found.
F4, primary well.
F5, secondary interior well.
