This question is closely related to, but more specific, than the question/comment that inspired it: Could a modern times time traveler produce an antibiotic in medieval times?.
Imagine a person is sent back in time to roughly middle-ages or slightly after, without warning to prepare for it. He has a high school and college education, but not in biology. Perhaps he a mild interest in science/biology; but ultimately is mostly limited to what is taught, and he retained, from college level intro to biology class.
He wants to create penicillin, for obvious reasons. He knows the general story of how it was discovered, specifically by accident on a loaf of bread and it was noticed that the mold killed bacteria near it (or at least that's how he remembers the story, it doesn't mater how accurate that memory is since that is what he is working off of when making plans). He has decided to use the below approach to try to discover and recreate it. Assume he has the funding of a king that he impressed with modern technology, his budget is not limitless since the king isn't convinced that he can recreate anything, but it's sufficiently high for him to work with assistance and all reasonable expense covered.
To try to create penicillin he first gets many types of bread, and other wheat and food products, and intentionally lets them get moldy. He uses multiple different locations to grow the mold, mostly in dungeons but some in other places that aren't dank and moldy just in case penicillin grows better in other locations. He also gets the local blacksmith to construct very basic petri dishes and starts to grow many different bacterial cultures for testing.
Once bacteria and fungus samples exist he will place part of his bacteria samples in a separate dish with some fungus. He will watch to see if the bacteria appears to die out. He doesn't yet have a proper microscope since he hasn't figured out what to ask for to build one yet (When could a microscope first be made?). However, if he cultured bacteria well there will be enough built up in his petri dish to be able to see their presence with the naked eye, and thus tell when they appear to be killed.
He also gets a number of poor saps to play guanine pig if needed. Perhaps he gets partial pardons for criminals that would have be hung otherwise if they agree to play test dummy. He isn't unethical enough to do anything he considers to have a high chance of killing anyone, but is willing to use them as test subjects for what he considers lower risk human trials, especially considering how much good the drug will do if successful.
If he gets a fungus that appears to be antibacterial he will have some of this test subjects try it to see rather it makes them ill. He tries both oral consumption and exposing it to an open wound. He would start in very tiny quantities and only work his way up to higher levels if his subjects appear unharmed, generally he is trying to treat the subjects well and make their working for him be a clear and significant benefit over the alternative.
He will use separate controls later to test larger quantities of the fungus to ensure his original subjects didn't build up unnaturally high immunities to it from constant exposure to lower quantities. He is also aware that test subjects may develop germs with immunity to his fungus and so will use different subjects for testing the effectiveness of his fungus in fighting disease.
Assuming positive results he moves on to larger controlled trials with peasants, in the same way that we would do control trials with a new antibiotic today, other then the lack of infrastructure and communication systems making it harder to do quite as large a scale as he would prefer.
He generally takes his times, uses controls (as much as he can given the small number of samples/subjects he is working with), and triple checks any apparent result before moving on. However, while he has a decent understanding of the scientific method and intelligent he is not a scientist, and may still forget to control for certain variables or otherwise make mistakes that come from doing a job he was never taught how to do properly.
My main question is, would this work? What are the odds of his discovering any antibiotic fungus, that is relatively safe for humans, using this approach? He doesn't know what he needs to do to recreate penicillin, and I doubt he would find the actual penicillin fungus, but surely there are other antibiotic fungus he could discover which would suffice?
Assuming the main question is answered, and that this approach can work, here are some follow up questions that would be nice to have feedback on. The remaining are not mandatory to answer this question, I can post separate questions for them if need be, but any feedback that one wishes to add addressing them is welcomed.
what are the odds of negative results of this experiment, and what sort of result could happen? How badly will his test subjects suffer from eating their moldy bread?
Even if he finds a good fungus how easy would it be to then culture, grow, deliver, and teach others how to use it such that it would prove effective in fighting infection? Would it have to be reserved for rich high-paying nobles because they can't culture enough for regular use? He will try to prevent overuse creating penicillin immune bacteria, but the implications of such immunities are off-topic enough to likely warrant their own question later.
how long would it be expected for this to take? Obviously this is more then a month's effort, but are we talking a year, a decade, or a lifetime?