Heat olive oil in frying pan over medium high heat. Add sliced courgettes and mushrooms; stir until tender, about 4 or 5 minutes. Add the tomatoes and cook for another few minutes until softened.
Beat the eggs with a fork; add grated Parmesan and salt. Pour this mixture over the vegetables and cook until the eggs are cooked at the side of the pan. Place a plate on top and flip the frittata over. Continue cooking on the other side until both sides are golden brown.