Transfer the omelette and the plastic wrap to a cutting board, keeping the nicest side facing down, so that it will be the outside of the purse. Cut it into a large, vertical rectangle, allowing the shorter sides to stay rounded, just slice off the sides. Then gently transfer this onto a serving plate, and spoon the mushroom filling into the centre. Sprinkle on as much shredded white cheddar cheese as you like. Fold up the omelette like a letter, with the seam near the top of the omelette.