Heat up the butter in a frying pan and saute the mushrooms until soft. Spread a spoonful of cheese on half of each tortilla leaving a 1cm margin around the edge. Top with the mushrooms. Brush the edges of the tortilla with beaten egg, then fold in half and push the edges firmly together to seal.
Pour vegetable oil into a deep frying pan to a depth of 1cm. Heat until a cube of bread goes brown in 1 minute - then fry the quesadillas, 2 or 3 at a time for 2 minutes on each side until browned. Drain on kitchen paper and serve with tomatoes, cucumber and coriander sprigs to garnish