Sauté the prepped mushrooms - Add the mushrooms to a dry pan and lightly salt them. Sauté the mushrooms until they release their water and become soft and silky. Set aside.
Sweat the leeks - Add a bit of olive oil to the pan, add the leeks, and sauté them until they are very soft and beginning to melt. Add the garlic and cook a minute or two until fragrant.
Prep the tomatoes and preheat the oven - Remove the core and seeds from the tomatoes and give them a rough chop, reserving a few sliced of tomato for the top of the pie. Preheat the oven to 350°, convection bake setting.
Combine the veg - Combine the leeks, chopped tomatoes, thyme and 1/2 t salt in a bowl and let stand for a few minutes to cool a bit. Then fold in the egg whites.
Assemble and bake - Sprinkle a bit of the parmesan on the parbaked pie crust, then pour in the vegetable mixture and spread it evenly. Top with the tomato slices and then the rest of the cheese. Bake for fifteen minutes or until the filling is set. Let stand for ten minutes before serving.