In a mixing bowl, combine flour and salt. Cut in butter until mixture resembles coarse crumbs. Stir in ice water, a tablespoon at a time, until dough forms. Wrap in plastic and refrigerate for 30 minutes.

In a large bowl, combine shredded turkey, Swiss cheese, spinach, mushrooms, beaten egg, milk, Dijon mustard, and black pepper. Mix well.

Preheat the oven to 375°F (190°C). Roll out the chilled dough on a floured surface to fit your baking dish. Place the dough in the dish and fill with the turkey mixture. Cover with another layer of rolled-out dough, sealing the edges.

Cut slits in the top crust for steam to escape. Bake for 35-40 minutes or until the crust is golden brown. Let cool for 10 minutes before cutting into squares.