Season the beef cubes with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the beef in batches and brown on all sides, about 3-4 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.
Sprinkle the flour over the onion and garlic, stirring constantly for 1-2 minutes to cook the flour.
Gradually whisk in the beef broth, scraping up any browned bits from the skillet. Stir in tomato paste, dried thyme, and dried rosemary. Bring to a simmer and cook until slightly thickened, about 3-4 minutes.
Pour the sauce over the beef in the slow cooker. Add sliced carrots, celery, frozen peas, frozen corn, and the bay leaf. 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).
Transfer the beef mixture from the slow cooker to a 9-inch oven-safe pie dish, removing the bay leaf.
Roll out the thawed puff pastry sheet to fit over the top of the pie dish. Place the pastry over the beef mixture and trim any excess. Press the edges to seal and cut a few small slits in the top to allow steam to escape.
Brush the beaten egg over the puff pastry to give it a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the pastry is puffed and golden brown.
Remove from the oven and let rest for 5 minutes before serving.