Saute the onion; mushrooms, garlic and herbs in the butter over medium heat until lightly browned, about 10 min. Spoon this mixture over 4 tortillas that have been placed on lightly greased cookie sheets.

Top each tortilla with broccoli and cheese and a second tortilla. Bake in a 350 oven until cheese melts, about 10 min. Cut each quesadilla into wedges to serve. Serves 4.