Make the pastry: Pulse Stilton, flour, butter, and salt in a food processor into pea-size crumbles. With the motor running, slowly add water; mix until dough forms. Flatten dough into a disk and wrap in plastic wrap; chill until ready to use.
Make the filling: Heat oven to 375°. Heat 1⁄4 cup oil in a 6-qt. Dutch oven over medium-high. Season beef with salt and pepper; working in batches, cook, turning as needed, until browned, 6–8 minutes. Transfer beef to a plate; set aside. Add garlic, chopped onion, the carrots, and celery to pan; cook until golden, 8–10 minutes. Add beer; cook until reduced by half, 5–7 minutes. Return beef to pan along with stock, 1 bay leaf, the rosemary, and thyme; boil. Cover and transfer to oven; cook until beef is very tender, 2–2 1⁄2 hours. Let beef cool; transfer to a cutting board and shred into bite-size pieces. Strain sauce into a bowl; stir in beef. Meanwhile, heat remaining oil in a 12" skillet over medium; cook sliced onions and remaining bay leaf until onions are caramelized, about 45 minutes. Stir in Worcestershire sauce; cook until evaporated, 2–3 minutes. Stir into beef mixture.
Assemble and bake the pie: Heat oven to 350°. Pour filling into a 2-qt. oval or 9" x 13" baking dish. On a lightly floured surface, roll pastry into a 13" x 17" rectangle, about 1⁄6" thick. Brush edges of baking dish with beaten egg. Place pastry over filling; trim excess. Use a fork to press pastry to the edges of plate. Brush top of pastry with egg and cut three slits in the top. Bake until pastry is golden brown and filling is bubbly, about 1 hour and 15 minutes.