Creating the delightful Irish Beef Pot Pie is straightforward if you follow these steps:

1. Preheat Oven: Set your oven to 375°F (190°C).

2. Brown the Beef: In a large skillet, heat olive oil over medium heat. Add the beef cubes and brown them on all sides. Remove the beef and set aside.

3. Sauté Vegetables: In the same skillet, add onions, carrots, and celery. Sauté until softened, about 5-7 minutes.

4. Add Garlic: Stir in minced garlic and cook for another minute until fragrant.

5. Make the Gravy: Sprinkle flour over the vegetables and mix well. Gradually add beef broth and stir continuously until the mixture thickens.

6. Add Seasoning: Include Worcestershire sauce, thyme, rosemary, salt, and pepper to the pan. Return the beef to the skillet, then stir in heavy cream and frozen peas. Bring the mixture to a gentle simmer.

7. Prepare the Pastry: Roll out the puff pastry on a floured surface. You can use a store-bought pastry or homemade.

8. Fill the Pie: Transfer the beef filling into a greased pie dish. Cover it with the puff pastry, trimming any excess. Cut a few slits in the top for steam to escape.

9. Brush with Egg: Beat the egg and brush it lightly over the pastry surface for a golden finish.

10. Bake: Place the pie in the preheated oven and bake for 30-35 minutes or until the pastry is golden brown and flaky.

11. Cool Before Serving: Allow the pie to cool for a few minutes before slicing. This helps the filling to set slightly, making it easier to serve.