Beef and Guinness Pie

Preheat oven to 325 degrees F and place oven rack in middle position.

In a large bowl, combine tomato paste, beef stock and Worcestershire sauce. Add beef, mushrooms, onions, garlic, thyme, and stout and stir well. Sprinkle flour over beef mixture, season to taste with salt and pepper, and stir.

Transfer to a deep pie dish and set on a large baking sheet. Cover dish with foil. Bake, stirring occasionally, until meat is very tender, 3 1/2 to 4 hours. Alternatively, place in a slow cooker for 6-8 hours on low, until beef is tender.

Beat egg and 1 tsp. water together in a small bowl and set aside. Roll puff pastry out on a lightly floured surface to a 1/4" thick circle, 2" wider than baking dish. Remove pie dish from oven and uncover. Drape pastry over dish and brush with egg wash. Return baking dish to oven and bake until pastry is puffed and golden brown, about 40 minutes.