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1. Start by heating the olive oil in a large, heavy-bottomed pot over medium-high heat. Once the oil is hot, add the beef cubes in batches, ensuring not to overcrowd the pot. Sear the beef on all sides until browned, about 5-7 minutes. Remove the beef and set it aside on a plate.
2. In the same pot, add the diced onion and cook for about 3-4 minutes until it becomes translucent. Stir in the minced garlic and cook for an additional minute until fragrant.
3. Add the diced carrots and celery to the pot, cooking for another 5 minutes until they start to soften. Then, toss in the sliced mushrooms and cook for an additional 3-4 minutes until they release their moisture and begin to brown.
4. Stir in the tomato paste, mixing well to coat the vegetables. Cook for about 2 minutes to deepen the flavor.
5. Return the seared beef to the pot, and pour in the beef broth and red wine (if using). Add the Worcestershire sauce, dried thyme, dried rosemary, salt, and pepper. Stir everything together, ensuring the beef is submerged in the liquid.
6. Bring the mixture to a gentle simmer, then reduce the heat to low. Cover the pot and let it cook for about 1.5 to 2 hours, stirring occasionally, until the beef is tender and the flavors meld together. If the sauce becomes too thick, you can add a bit more broth or water.
7. Once the beef is tender, remove the lid and increase the heat to medium-high. Allow the filling to simmer uncovered for about 10-15 minutes to reduce and thicken the sauce. Stir occasionally to prevent sticking.
8. If you prefer a thicker filling, you can mix 1 tablespoon of cornstarch with 2 tablespoons of cold water to create a slurry. Stir this into the filling and cook for an additional 2-3 minutes until thickened.
9. Once thickened, taste the filling and adjust the seasoning with more salt and pepper if needed. Remove the pot from heat and let it cool slightly while you prepare the pastry.
10. Preheat your oven to 400°F (200°C).
11. On a lightly floured surface, roll out one sheet of puff pastry to fit your pie dish. Make sure it’s large enough to cover the bottom and sides of the dish. If you’re using a round dish, aim for a circle that’s about 2 inches larger than the dish itself.
12. Carefully transfer the rolled pastry into the pie dish.
13. Brush the top of the pastry with the beaten egg to give it a beautiful golden color when baked.
14. Place the pie in the preheated oven and bake for 25-30 minutes, or until the pastry is golden brown and puffed up.
15. Once baked, remove the pie from the oven and let it cool for about 10 minutes before slicing and serving. Enjoy your delicious beef pot pie!

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