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 5 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add diced onion and cook for 3 minutes until softened. Add minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 1-2 minutes to cook the flour.
Slowly whisk in the beef broth, making sure there are no lumps. Stir in tomato paste, dried thyme, and dried rosemary. Cook for 2-3 minutes until the mixture thickens slightly.
Pour the mixture over the beef in the slow cooker.
Add sliced carrots, celery, frozen peas, frozen corn, and bay leaf to the slow cooker. Stir gently to combine.
Cover and cook on low for 6 hours, or until the beef is tender and vegetables are cooked through.
About 30 minutes before serving, preheat the oven to 400°F (200°C).
Remove the bay leaf from the slow cooker filling and stir gently.
Transfer the beef and vegetable filling to an oven-safe baking dish.
Roll out the thawed puff pastry sheet to fit the top of the baking dish. Place the pastry over the filling, trimming any excess edges.
Brush the beaten egg over the puff pastry to give it a golden color when baked.
Bake in the preheated oven for 25-30 minutes, or until the puff pastry is puffed and golden brown.
Remove from oven and let rest for 5 minutes before serving.