Heat 1 tablespoon oil in pan over high heat; Add meat until cooked through. Set meat aside on a plate. Salt to taste.
Add 1 tablespoon of olive oil to the pan. Add onions and mushrooms, stir fry until cooked through. Add meat mixture to combine all the flavours, then set aside.
To assemble quesadillas sprinkle ¼ cup of cheese over half of each tortilla. Top each tortilla with meat and mushroom mixture then sprinkle each again with ¼ cup of the remaining cheese. Fold tortilla in half pressing gently.
Heat sandwich press adding 1 teaspoon of oil. Once hot, place the folded tortilla on the press for approximately 2 minutes or until golden. Repeat the process with each tortilla.
