Put oven rack in middle position and preheat oven to 350°F.
Pat beef dry. Stir together flour, salt, and pepper in a shallow dish. Add beef, turning to coat, then shake off excess and transfer to a plate. Heat oil in a wide 5- to 6-quart ovenproof heavy pot over moderately high heat until just smoking, then brown meat, turning occasionally,about 5 minutes, then transfer to a bowl.
Add onion, garlic, and water to pot and cook, scraping up any brown bits from bottom of pot and stirring frequently, until onion is softened, about 5 minutes. Add tomato paste and cook, stirring, 1 minute. Stir in beef with any juices accumulated in bowl, broth, beer, Worcestershire sauce, peppercorns, and thyme and bring to a simmer, then cover and transfer to oven. Braise until beef is very tender and sauce is thickened, about 1 1/2 hours. Discard thyme and cool stew completely, uncovered, about 30 minutes.
Put a shallow baking pan on middle rack of oven and increase oven temperature to 425°F.
Divide cooled stew among bowls (about 3/4's full). Roll out pastry dough on a lightly floured surface with a lightly floured rolling pin into a 13-inch square, about 1/8 inch thick. Trim edges and cut dough into quarters. Stir together egg and water and brush a 1-inch border of egg wash around each square. Invert 1 square over each bowl and drape, pressing sides lightly to help adhere. Brush pastry tops with some of remaining egg wash for a beautiful golden top.
Bake pies in preheated shallow baking pan until pastry is puffed and golden brown, about 20 minutes.