01 - Heat vegetable oil in a large Dutch oven over medium-high heat. Season beef cubes with salt and pepper, then brown in batches until well-seared. Remove beef and set aside.
02 - In the same pot, add onion, carrots, and celery; cook for 5 minutes until softened. Add garlic and cook for an additional 1 minute.
03 - Stir in tomato paste and cook for 2 minutes. Sprinkle flour over the vegetables and stir thoroughly to coat evenly.
04 - Gradually add beef broth and red wine while scraping up browned bits from the pot. Return browned beef to the pot. Stir in thyme, rosemary, and bay leaves.
05 - Bring mixture to a simmer, cover, and cook over low heat for 1.5 hours until beef is tender and sauce has thickened.
06 - Remove bay leaves, stir in frozen peas, and adjust seasoning with salt and pepper as needed. Allow filling to cool to room temperature.
07 - In a mixing bowl, combine flour and salt. Cut in cold butter until mixture resembles coarse crumbs. Gradually add ice water, mixing lightly just until dough forms. Divide dough in half, shape each into a disc, wrap tightly, and chill for 30 minutes.
08 - Preheat oven to 400°F. Roll out one dough disc on a floured surface to fit a 9-inch pie dish. Line the dish with the dough and fill with the cooled beef mixture.
09 - Roll out the second dough disc and cover the pie. Trim excess dough, crimp edges to seal, and cut small slits on top to allow steam to escape. Brush entire crust with beaten egg wash.
10 - Place pie in the oven and bake for 35 to 40 minutes until the crust is golden brown. Cool slightly before serving.