Finely chop the onion, garlic and jalapeño. Heat a small amount of oil in a hot pan. Sauté onions, then the garlic, until translucent. Add the mushrooms and jalapeño (adding more or less as desired) and cook until soft.
Soften the goat cheese by adding the milk and using a fork mix it to dissolve any lumps.
For each quesadilla, heat one side of the tortilla for 10 seconds on a hot frying pan using no oil. Turn over and immediately spread cheese and then place mushroom mix evenly on the tortilla. Fold the tortilla in half and leave in the pan, turning occasionally, until tortilla is crunchy.