01 - Set the oven temperature to 375°F.
02 - Toss beef cubes with 2 tablespoons flour, salt, and pepper until evenly coated.
03 - Heat vegetable oil in a large Dutch oven over medium-high heat. Brown beef in batches and set aside.
04 - In the same pot, add diced onion, carrots, and celery. Cook for 5 minutes until softened. Add minced 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 90 minutes until beef is tender and sauce thickens. Remove bay leaf and let filling 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, mixing until dough forms. Divide into two discs, wrap in plastic, and chill for at least 30 minutes.
08 - Roll out one dough disc on a floured surface to fit a 9-inch pie dish. Place dough in dish and trim edges.
09 - Spoon cooled beef filling evenly into the prepared crust.
10 - Roll out second dough disc and place it over the filling. Seal and crimp edges. Cut slits in the top crust to allow steam to escape.
11 - Brush the top crust with beaten egg to achieve a golden finish during baking.
12 - Bake the pie in the preheated oven for 40 to 45 minutes until the crust is golden brown.
13 - Allow the pie to rest for 10 minutes before slicing and serving.