Using a pastry cutter or a fork, mix flour and butter until crumbly. Add cheese, salt and water and blend until the dough just starts to come together. It will still be quite sticky. Form a ball, cover with plastic wrap, and refrigerate for about half an hour. Roll out and transfer to a pie plate.
Brush egg yolk onto crust, sprinkle bread crumbs on top and arrange tomatoes on top of that. Leave a wide border around the outside.
Sprinkle goat cheese on top and fold the edges of the pastry over the tomatoes.
Bake 30-40 minutes, remove from oven, and sprinkle with olive oil and basil.