Pat beef cubes dry, season with salt and pepper, then toss in flour until lightly coated.
Heat olive oil in Dutch oven over medium-high heat. Sear beef in batches until deeply browned, about 3-4 minutes per batch, then remove and set aside.
In the same pot, cook onion, carrots, and celery for 5-6 minutes until softened. Add garlic and cook 30 seconds until fragrant.
Stir in tomato paste and cook 1 minute to darken. Return beef and juices to the pot, then add beef stock, stout, Worcestershire sauce, thyme, and bay leaf.
Bring to a simmer, reduce heat to low, cover, and cook 1 hour 15 minutes until beef is tender. Remove bay leaf and adjust seasoning.
Let filling cool for at least 20 minutes before assembling the pie.
Preheat oven to 400°F. Roll out one pastry sheet and line the pie dish. Spoon in cooled filling.
Top with second pastry sheet, trim excess, and crimp edges to seal. Cut slits in the top crust to vent steam.
Brush top with beaten egg wash. Place pie on a baking sheet and bake 35-40 minutes until golden and filling bubbles through slits.
Rest the pie for 10-15 minutes before slicing to allow the filling to set.