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