Season the beef cubes with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the beef cubes in batches and brown on all sides, about 4-5 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add diced onion and cook for 3-4 minutes until softened. Add minced garlic and cook for 1 minute more. Transfer onion and garlic to the slow cooker.
Add sliced carrots, celery, frozen peas, all-purpose flour, beef broth, Worcestershire sauce, dried thyme, and dried rosemary to the slow cooker. Stir to combine all ingredients.
Cover and cook on low for 6 hours, or until the beef is tender and the sauce has thickened.
Preheat the oven to 400°F (200°C).
Transfer the beef and vegetable mixture from the slow cooker to a 9-inch pie dish.
Place the thawed pie crust over the filling, trimming any excess dough and pressing the edges to seal. Cut a few small slits in the crust to allow steam to escape.
Brush the pie crust with the beaten egg.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown and crisp.
Remove from the oven and let rest for 5 minutes before serving.