01 - Set the oven to 375°F.
02 - Toss beef cubes with flour, salt, and pepper to coat evenly.
03 - Heat vegetable oil in a large Dutch oven over medium-high heat. Brown the beef in batches and set aside.
04 - Add onion, carrots, and celery to the pot and cook for 5 minutes until softened. Stir in garlic and cook for an additional minute.
05 - Return beef to the pot. Stir in tomato paste, then pour in red wine and beef stock. Add Worcestershire sauce, dried thyme, and bay leaf.
06 - Bring mixture to a simmer, cover, and cook on low heat for 1.5 hours until beef is tender and sauce has thickened. Remove bay leaf and allow filling to cool slightly.
07 - In a large bowl, mix flour and salt. Rub in cold butter until the mixture resembles coarse crumbs. Gradually add ice water until dough forms. Divide into two discs, wrap in plastic, and refrigerate for at least 30 minutes.
08 - Roll one dough disc on a floured surface to fit a 9-inch pie dish. Place dough in dish and trim excess.
09 - Spoon cooled beef filling evenly into the crust.
10 - Roll out second dough disc and place over filling. Seal and crimp edges, then cut slits on top to vent steam.
11 - Brush the top crust with beaten egg.
12 - Bake for 40 to 45 minutes until the crust is golden brown.
13 - Allow the pie to rest for 10 minutes before slicing and serving.