There is nothing that inherently makes this impossible but it is very unlikely.

1) Organization and planning. There were no building codes in the middle ages. You would have to have an organization that managed city planning. City planning was not unheard of in the middle ages but it was never this robust. You have a good start making it a religious requirement, but you would also need the governing power to be on board as well. Forcing this is going to cost the powers that be to enforce and implement.

Considering the peasants made due with what was available to build there homes...well you are going to have to figure out how they are going to make peasants create things a certain way and whether are not they are going require standardized sizes and building materials.

2) Location is going to matter. A city on a plain could probably achieve this but in most cases in the medieval era you would not build on a wholly exposed plain. Its hard to defend. At a minimum you are probably going to need to deal with a coastline or a river. Medieval technology didn't allow city planners to alter the landscape like we can today. If you look at maps of ancient cities, Athens for example, you see that ancient cities followed the lay of the land.

3) Building round is fine. The technology required to build round is no major hindrance here. Its less efficient and more time consuming potentially but that's about all. Stone is going to be more difficult, but with wood you can set posts in place and then bend saplings in a circle. At that point the walls can be thatch or clay or mud brick or whatever, take your pick. There are plenty of examples of round dwellings from yurts to thatch.

4) Planning considerations. You should alter your city design to ensure transportation, communication, drainage and sanitation etc can be effectively managed. A spoke and wheel design allows you to be round and efficient. A design like this could serve you well.

Keep in mind the further from center you get the larger the distance you have to travel to hit one of the spokes. As such you are probably going to want more than 4.

There is nothing that inherently makes this impossible but it is very unlikely.

1) Organization and planning. There were no building codes in the middle ages. You would have to have an organization that manages city planning. City planning was not unheard of in the middle ages but it was never this robust. You have a good start making it a religious requirement, but you would also need the governing power to be on board. Forcing this is going to cost the powers that be to enforce and implement.

Considering peasants made due with what was available to build their homes...well you are going to have to figure out how they are going to make peasants create things a certain way and whether are not they are going require standardized sizes and building materials.

2) Location is going to matter. A city on a plain could probably achieve this but in most cases in the medieval era you would not build on a wholly exposed plain. Its hard to defend. At a minimum you are probably going to need to deal with a coastline or a river. Medieval technology didn't allow city planners to alter the landscape like we can today. If you look at maps of ancient cities, Athens for example, you see that ancient cities followed the lay of the land.

3) Building round is fine. The technology required to build round is no major hindrance here. Its less efficient and more time consuming potentially but that's about all. Stone is going to be more difficult, but with wood you can set posts in place and then bend saplings in a circle. At that point the walls can be thatch or clay or mud brick or whatever, take your pick. There are plenty of examples of round dwellings from yurts to thatch.

4) Planning considerations. You should alter your city design to ensure transportation, communication, drainage and sanitation etc can be effectively managed. A spoke and wheel design allows you to be round and efficient. A design like this could serve you well.

Keep in mind the further from center you get the larger the distance you have to travel to hit one of the spokes. As such you are probably going to want more than 4.