In a medium-sized bowl, sift the flour and the salt. With a pastry cutter or a fork, cut in the shortening until the mixture resembles coarse crumbs. Sprinkle in the water, 1 tablespoon at a time, mixing lightly with a fork until the pastry is just moist enough to hold together. Shape it into a ball.
Preheat the oven to 425°F.
Melt the butter in a large skillet over medium heat. Add the onions and garlic and cook until the onions are translucent. Lower the heat to low and cover the pan and cook slowly until caramelized, about 20 minutes.
Line a large cookie sheet with parchment paper. Roll out the pastry to 1/8-inch thick and transfer it to the parchment paper. Sprinkle on the onions and garlic evenly, leaving a border around the edge. Scatter the tomatoes on top, and then the cheese. Grind the pepper on top and sprinkle on the parsley. Fold the border up onto the filling. Brush the border with the egg and sprinkle with the Parmesan cheese. Bake in the preheated oven for 30 minutes or until golden.