Step 1: Brown the Beef

1. Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
2. Pat the beef cubes dry with paper towels, season generously with salt and pepper, and sear in batches until browned on all sides. Remove the beef and set it aside.

Step 2: Sauté the Vegetables

1. Add the onion, carrots, and celery to the same pot. Sauté for 5-7 minutes until softened.
2. Stir in the garlic and cook for another 1 minute until fragrant.

Step 3: Build the Flavor

1. Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes to eliminate the raw flour taste.
2. Add the tomato paste and mix thoroughly.

Step 4: Deglaze with Guinness

1. Pour in the Guinness stout, scraping up any browned bits from the bottom of the pot.
2. Return the beef to the pot, along with the beef broth, Worcestershire sauce, thyme, and bay leaf.

Step 5: Braise the Beef

1. Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 1 1/2 to 2 hours, or until the beef is tender and the sauce has thickened. Stir occasionally to prevent sticking.

Step 6: Final Touches to the Filling

1. Stir in the peas and cook for another 5 minutes. If the filling is too thin, stir in the cornstarch slurry and simmer until thickened. Adjust seasoning with salt and pepper as needed.
2. Remove the bay leaf and let the filling cool slightly.

Step 7: Assemble the Pot Pie

1. Preheat your oven to 400°F (200°C).
2. Transfer the beef filling to a deep pie dish or casserole dish.
3. Roll out the puff pastry or pie crust and place it over the filling, pressing the edges to seal. Trim any excess dough and crimp the edges decoratively.
4. Cut a few small slits in the top to allow steam to escape. Brush the crust with the beaten egg for a golden finish.

Step 8: Bake

1. Bake the pot pie in the preheated oven for 25-30 minutes, or until the crust is golden brown and flaky.
2. Let it cool for 10 minutes before serving to allow the filling to set.