Heat olive oil over medium heat, and cook onion until softened.
Add mushrooms and cook about 5-10 minutes.
Add spinach, cook until most of the liquid is gone.
Add potatoes.
Add mashed beans, and a dash of salt and pepper.
Stir together, and cook for about five minutes. Turn off heat to mixture.
Preheat large skillet, flat grill top, grilling machine etc.
Evenly divide filling on one-half of each burrito. Evenly divide cheese amongst filling. Fold other half of burrito over filling, and gently press.
Spray non-stick spray on cooking surface (if necessary), and cook the quesadilla for 2-3 minutes a side, just until it starts to color. Flip and repeat on other side.
Remove to cooling rack or other flat surface. Cool for one minute, cut into triangles with knife or pizza cutter.
Serve with or without flavored dressing.