How to get quesadillas to stick closed without cheese
Quesadilla literally means &quot;little cheese.&quot; A quesadilla without cheese isn't a quesadilla. It's a tortilla folded in half with stuff inside.
To get a folded-in-half tortilla to stick together without cheese, try eggs. Put the open tortilla in the pan, then pour a thin layer of beaten eggs on top. Cook slowly until the eggs start to solidify but are still wet on top. Then fold the tortilla in half. The raw layer of eggs should stick to itself when it finishes cooking.

Note: I haven't tried this myself, so I don't have exact quantities and timing figured out. This idea is based on a recipe for breakfast egg wraps where the eggs are poured into the pan first, then cooked until somewhat solid but still wet on top, then a tortilla is placed on top so it sticks to the raw eggs. Then the whole thing is flipped over, so the tortilla gets nice and crispy and the egg finishes cooking. That recipe used one egg per tortilla (but didn't specify what size of tortilla). The challenge with the modification I suggested above will be getting the eggs fully cooked without burning the tortilla. It's a bit like cooking an omelet, but with an omelet you can put on a lid and use steam to help cook the eggs, whereas you probably don't want to do that here because it will make the tortilla soggy. I think it should be possible with a low heat and a very thin layer of eggs. If you get it to work, please share what combination of timing, temperature and quantities worked best.