Preheat oven to 450 degrees F (230 degrees C). Press puff pastry sheet into the bottom and up the sides of a shallow casserole dish or 8-inch pie plate.
Beat milk, eggs, spinach, salt, and pepper together in a bowl. Spread a thin layer of cheese onto the pastry crust in the baking dish; sprinkle ham over the top. Pour egg mixture over ham and sprinkle remaining cheese over the top. Arrange tomato slices over the cheese.
Bake in the preheated oven for 20 minutes. Reduce oven temperature to 350 degrees F (175 degrees C) and continue baking until crust is browned, about 30 minutes more.