01 - Set the oven temperature to 375°F.
02 - Heat vegetable oil in a large Dutch oven or heavy pot over medium-high heat. Brown beef cubes in batches on all sides, then remove and set aside.
03 - Add diced onion, carrots, and celery to the pot and cook for 5 minutes until softened. Stir in minced garlic and cook an additional minute.
04 - Incorporate tomato paste and all-purpose flour, cooking for 1 to 2 minutes to remove raw flour taste.
05 - Return beef to the pot. Pour in beef broth and dry red wine. Add thyme, rosemary, bay leaves, salt, and black pepper. Bring mixture to a simmer.
06 - Cover and simmer gently for 1 hour 30 minutes, stirring occasionally, until beef is tender.
07 - Stir in frozen peas, remove bay leaves, and adjust seasoning as needed. Allow filling to cool slightly.
08 - Line a 9-inch pie dish with one sheet of puff pastry. Fill with the beef mixture. Cover with the second pastry sheet, trim excess, and crimp edges to seal.
09 - Cut slits in the top pastry to allow steam to escape and brush surface with beaten egg.
10 - Bake for 35 to 40 minutes until the pastry is golden and crisp.
11 - Allow the pie to rest for 10 minutes before slicing and serving.