Sauté mushrooms and shallot in a nonstick skillet until the liquid is just about evaporated. Set aside to cool.
Preheat oven to 400F. Unfold 1 pastry sheet on each of 2 baking sheets.
Top pastry with ham, cheese and mushrooms, leaving ½-inch border. Whisk eggs, rosemary, pepper, salt and nutmeg in bowl. Whisk in sour cream. Spoon egg mixture over toppings on each pastry.
Bake until pastries are puffed and golden and toppings are set, about 25 minutes.