My standard caveat: Europe is big, 'medieval' is a long time. This answer mostly describes 14th century England, and other places varied to some degree (but, among peasants, not so much).

There are a few factors at play here. First and foremost is that the preparation of food for the peasantry was very much dependent on what implements they had, and what fuel they had.

It's sometimes quite difficult for us to imagine how few possessions medieval people had, even those who were moderately well off. One of the places in which we can see this clearly are wills, in which all someone's possessions, down to "my third best shirt" or the like are often ennumerated and distributed to relatives, and it can very often be done in six or eight lines of text. For instance, to pull out an example from recent stuff I've read, an English barber, John Chesman, who died in 1509, left tables and kitchen stuffs to his fianceé: "ij pewder dublers, ij dishis, ij sawsers, a new saltseller of pewder, iiij candilstikes of laton, a posnet of laton, ij meslynes pannys, a bigar and a les, a new ladyll of laton" (spelling per original). Chesman was by no means a peasant, but we're still looking at about six kitchen implements in total.

There aren't the same records for peasants, of course - there never are - but we can work from archaeological remnants and say with reasonable accuracy that a peasant household that had one earthenware cooking pot, a knife, and a wooden spoon and bowl per person was doing pretty well. So if you have one pot, then one-pot dishes like pottage are what you can do, and there's not much option.

Next, there's the question of fuel. Firewood wasn't free, or rather, you paid for it in labour costs of finding it (usually deadwood, for peasants who weren't allowed to cut down trees), and bringing it home. And when every peasant household in the neighbourhood was doing this every day, you had to go some distance and expend some effort. So when you got the firewood home, you wanted to use it as efficiently as possible - and when it comes to efficiency, it's hard to beat boiling things in a pot. It is vastly more efficient than roasting meat by a fire, for example. Frying is difficult in earthenware pots, and fried food doesn't go as far as a pottage.

Speaking of how far it had to go, there's the actual food available. This might have included some meat (more in autumn, less in the rest of the year), and some foraged greens and roots, and probably some sort of brassicas, carrots, etc grown in a kitchen garden. And then some grain - barley or oats, in some form, or possibly breadcrumbs, which were present to thicken the pottage as much as to provide carbohydrates. The pottage, where you put everything in a pot, add water, and boil it, ensures that you can stretch the food a bit further to feed a larger number of people.

Bread, of course, could not be produced in the average peasant household - since there was no oven - so bread came from the local landlord as part of wages or even handouts, or was bought from the local baker. In the poorer houses, this would have been the previous day's bread, which would also have served as a bowl, with the top torn off and the crumb removed. Once the pottage had soaked into the bread, you'd eat your 'bowl' as well.

So the actual content of the pottage - which is a catchall word literally meaning 'cooked in a pot' covered everything from very simple gruels (possibly more common in Ireland than elsewhere) up to fairly dense, relatively meaty stews in autumn, when animals were slaughtered.

However... (finally getting back to your question) choice of food didn't happen for anyone, really. You cooked what was available, and that's what there was to eat. Taverns, such as they were, served one dish, and if you didn't like it, there was probably bread. Even in the biggest noble households, only the head of the household got to choose what they might eat, and even then, it was a very limited choice. Feasts, when served, were essentially "we killed all these animals and cooked them", rather than any more variation of food from the norm. The situation we have where you can choose from many different things and cook what you'd like to have is pretty new in human history, being essentially only available from the Industrial Revolution.

References:

Lisa Jane Howarth Liddy, Domestic Objects in York c. 1400–1600: Consumption, Neighbourhood and Choice (Unpublished PhD thesis, 2015)

Peter Brears, Cooking and Dining in Medieval England (2012)

Barbara A. Hanwalt, The Ties That Bound: Peasant Families in Medieval England (1988)

Vera. K. Ninez, Household Gardens: Theoretical Considerations on an Old Survival Strategy (1984)