How to Make It
Preheat oven to 340°F. Season beef generously with salt and pepper. In a large Dutch oven or heavy pot, heat the oil over moderately high heat. Add beef and cook, turning occasionally, until browned all over, about 12 minutes. Transfer beef to a plate; drain oil from pot and discard oil.
Return pot to moderately high heat and add butter, carrots, onion, parsnip, celery, rutabaga, mushrooms, garlic, rosemary, and bay leaves. Cook, stirring occasionally, until just tender, about 10 minutes. Add tomato paste and cook, stirring, 4 minutes. Add wine and boil until liquid is reduced by half, about 8 minutes.
Return the beef and any accumulated juices to pot. Add stock; bring to a boil. Cover and transfer to preheated oven. Braise until beef is very tender, about 2 hours and 45 minutes. Carefully remove beef from the braising liquid to a cutting board and let cool slightly. Cut beef into bite-size pieces and return to pot; season with salt and pepper.
Increase oven temperature to 400°F. Using top of a 5-inch bowl as a guide, cut 6 rounds from pastry. Transfer rounds to a parchment paper–lined baking sheet. Freeze until firm, about 15 minutes. Brush pastry with egg wash. Bake until pastry is golden, 10 to 12 minutes; cool.
Ladle the hot stew into bowls and top each with a pastry round. Serve immediately.