01 - Preheat the oven to 375°F (190°C).
02 - Heat vegetable oil in a large Dutch oven or heavy pot over medium-high heat. Brown the beef in batches on all sides. Remove and set aside.
03 - Add diced onion, carrots, and celery to the pot. Sauté for 5 minutes until softened. Add minced garlic and cook for an additional minute.
04 - Stir in tomato paste and all-purpose flour; cook for 1 to 2 minutes to remove raw flavor.
05 - Return beef to the pot. Pour in beef broth and dry red wine. Add dried thyme, dried rosemary, bay leaves, salt, and black pepper. Bring to a simmer.
06 - Cover and simmer gently for 1.5 hours, stirring occasionally, until beef is tender.
07 - Stir in frozen peas, remove bay leaves, and adjust seasoning if necessary. Allow the filling to cool slightly.
08 - Line a 9-inch pie dish with one sheet of puff pastry. Fill with the beef mixture.
09 - Cover filling with the second sheet of pastry, trim excess, and crimp edges to seal. Cut slits on the top to allow steam to escape. Brush with beaten egg.
10 - Bake for 35 to 40 minutes until the pastry is golden brown and crisp.
11 - Allow the pie to rest for 10 minutes before slicing and serving.