Preheat oven to 400°; place rack in middle. Whisk egg with water in a bowl. Unfold puff pastry sheets on floured surface and roll out. Transfer to parchment paper-lined pan and pierce with a fork. Cut 4 circles out of each sheet with a 4-inch round cutter; cut holes in centers of circles, and discard middles. Stack 3 rings on top of each other, brushing top of each with egg wash; bake 15 minutes. Toss shrimp with crushed red pepper, 1/8 teaspoon salt, and black pepper. Sauté shrimp in 2 teaspoons olive oil for 2 minutes; set aside. Add 1 teaspoon olive oil to pan, and sauté carrot, celery, mushrooms, and thyme sprigs for 10 minutes. Add 1 tablespoon olive oil and flour; stir for 2 minutes. Add wine; simmer for 2 minutes. Add milk, and simmer for 5-10 minutes. Stir in shrimp and 1/4 teaspoon salt and white pepper. Ladle shrimp mixture evenly into pastry bowls.