Heat oil in a large frypan over a high heat and add the mushrooms. Sauté for 3-4 minutes to soften and allow them to become lightly golden. Season with salt and pepper. Add the garlic and parsley and cook for a further minute.
Sprinkle half of the cheese on four of the tortillas. Divide the mushroom mixture on top and then the remaining cheese. Sandwich the last 4 tortillas on top.
Brush the quesadilla with oil and heat a large pan over a medium heat. Working with one quesadilla at a time, cook for 1-2 minute until golden and the cheese begins to melt. Carefully flip and cook for a further 1-2 minutes. Repeat with the remaining. Cut into quarters and serve with a cheek of lime.