1. Cook the lamb: Heat olive oil in a large skillet over medium-high heat. Add the ground American lamb, breaking it up with a spoon, and cook until browned, about 5 minutes.

Remove the lamb with a slotted spoon and set aside, leaving the fat in the pan.

2. Sauté the vegetables: In the same skillet, add the onion, carrots, and celery. Cook until softened, about 5 minutes.

Stir in the garlic and tomato paste, cooking for another minute until fragrant.

3. Build the flavor: Return the lamb to the pan. Stir in Worcestershire sauce, Dijon mustard, thyme, rosemary, smoked paprika, salt, and pepper.

Sprinkle the flour over the mixture and stir to coat, cooking for 1-2 minutes.

4. Deglaze with Guinness: Pour in the Guinness, scraping up any browned bits from the bottom. Let it simmer for 2 minutes.

Add the beef broth and bring to a gentle simmer. Cook uncovered for 15-20 minutes, stirring occasionally, until thickened.

Stir in the frozen peas and remove from heat. Taste and adjust seasoning.

5. Assemble the pie: Preheat oven to 400°F (200°C). Transfer the filling to a pie dish or baking dish. Lay the puff pastry over the top, trimming any excess. Press the edges to seal and cut a few slits in the top for steam to escape. Brush with the beaten egg and sprinkle with flaky salt.

6. Bake: Bake for 25-30 minutes, until the pastry is golden brown and crispy.

7. Serve:Let the pie cool for 5-10 minutes before serving.