1. Crust: In the bowl of a food processor, combine flour and salt. Add butter and cheese and pulse until the mixture resembles coarse meal.

2. With machine running, drizzle ice water in a slow, steady stream through feed tube. Pulse until dough holds together without being wet or sticky; be careful not to process more than 30 seconds. To test, squeeze a small amount together; if it is crumbly, add more ice water, 1 tablespoon at a time.

3. Gather dough into a ball and flatten into a disc. Wrap in plastic. Transfer to the refrigerator and chill at least 1 hour. Dough may be stored, frozen, up to 1 month.

4. Filling: Heat oil in a large pot over medium. Add bacon and cook until crisp and browned, about 14 minutes. Remove with a slotted spoon and drain on paper towels. Pour fat into a bowl and reserve.

5. Wipe out pot with paper towels. Add 2 tablespoons reserved fat to pot and heat over medium-high until hot.

6. Season beef with 2 teaspoons salt and 1 teaspoon pepper. Working in 3 batches, cook beef until browned on all sides, about 4 minutes per batch. Using a slotted spoon, transfer beef to a large bowl. Add more reserved fat between batches if needed.

7. Pour fat from pot into the bowl of reserved fat. Add 1 cup broth to pot, and cook, stirring and scraping bottom, 1 minute. Pour over meat.

8. Heat 2 tablespoons reserved fat in pot over medium-high. Add onions and garlic and cook until onions soften and garlic is fragrant, about 2 minutes. Stir in mushrooms and cook, 3 minutes. If bottom of pot begins to burn or onions begin to stick, stir in about 1/4 cup of the remaining broth. Sprinkle flour over vegetables, add mustard, and cook, stirring constantly, 1 minute.

9. Return beef and broth to pot. Add remaining broth, stout, thyme, and bay leaf. Bring to a boil, scraping flour mixture from bottom and sides of pot. Reduce heat and simmer partially covered, stirring occasionally, 1 hour 30 minutes.

10. Add potatoes. Cover and simmer until potatoes are tender but not mushy, about 25 minutes. Remove and discard bay leaf and thyme. Stir in bacon, pearl onions, dill, horseradish, and vinegar. Season with salt and pepper. Transfer to a 2 1/2-quart baking dish and place on a rimmed baking sheet. (Filling can be made up to 2 days ahead and refrigerated. Bring to room temperature before baking.)

11. Preheat oven to 400 degrees. On a floured work surface, roll out dough to a diameter about 2 inches larger than baking dish. Center dough over filling; trim edges to about 1-inch overhang (it's okay if it's a little uneven). Brush egg wash over bottom of edges, and press to baking dish to seal. Brush remaining egg wash over top of pie. Cut vents in center. Bake until crust is golden brown and the filling bubbles, 35 to 45 minutes. Let cool 20 minutes before serving.