In a food processor, pulse together the flour, salt and sugar.
Add the butter cubes, and pulse the butter until incorporated and the mixture looks like dense cornmeal.
Add the water 1 Tbs. at a time and pulse, adding more water as needed until the dough comes together. It should be moist but not sticky.
Shape the dough into a flat disc, wrap in plastic wrap, and refrigerate for 20 minutes or more. Can be made ahead.
On a well floured surface, roll out the dough so that it fits into a 10 in. tart pan with a removable bottom. Prick the bottom of the crust and refrigerate until needed.
Preheat oven to 400 degrees
Melt butter in a large skillet, Add the leeks, mushrooms, 1/2 tsp. of the salt, and 1/4 tsp. of the pepper. Saute until leeks are soft, and mushrooms start to brown, about 5 minutes. Place mixture in a bowl to cool for 15 minutes while you prep the remaining ingredients.
Add the remaining ingredients, including the balance of salt and pepper to the bowl and mix well.
Spread the filling in the tart shell and bake until brown and bubbly, about 22-25 minutes.