Mix the flour with the cold butter until you get crumbs. Add the egg, water and salt. Knead a dough. Cover it with plastic wrap and leave it in the fridge for about 30 min.
Braise the mince in a pan and stir until it crumbles into fine pieces. Chop the onions and 2 peppers finely. Add them to the mince and fry them as well. Season with black pepper and paprika.
Roll out the dough into a diameter a little larger than that of the baking dish you're going to bake the pie in. Press it firmly to the walls and remove the excess edges of dough with a rolling pin.
Distribute the mince evenly and cover it with the cheese you've grated ahead of time. On top, arrange round slices of tomatoes and the remaining pepper.
Sprinkle with savory and bake in a preheated 356°F (180 °C) oven until the dough reddens and cheese crisps.