Sauté the Aromatics

1. In a large skillet over medium heat, heat the olive oil until shimmering.
2. Add diced onion and celery; cook until softened, about 4–5 minutes.
3. Stir in the minced garlic and cook for 30 seconds more until fragrant.

Cook the Meat

1. Add ground beef or lamb, breaking it apart with a wooden spoon as it browns.
2. Continue cooking until no longer pink and most of the moisture has evaporated.

Season and Thicken

1. Stir in Worcestershire sauce, tomato paste, rosemary, thyme, salt, and pepper.
2. Sprinkle the flour evenly over the mixture; stir and cook for about 1 minute to remove the raw flour taste.

Add Wine, Broth, and Vegetables

1. Pour in the red wine and simmer for 2–3 minutes to reduce slightly.
2. Add the beef broth and stir to combine.
3. Stir in peas and carrots, cooking until the sauce thickens a bit, about 5 minutes.
4. Remove from heat.

Prepare the Potato Topping

1. If using leftover mashed potatoes: Warm slightly, then mix in Cheddar, Parmesan, and egg yolks until smooth and creamy.
2. If making from scratch:
3. Boil the peeled, diced potatoes in salted water until tender, about 15 minutes. Drain well.
4. Mash with cream, butter, salt, and white pepper until smooth.
5. Stir in Cheddar, Parmesan, and beaten egg yolks.

Assemble the Pie

1. Preheat oven to 400°F.
2. Spoon the beef and vegetable mixture into a 2-quart casserole or deep pie dish.
3. Spread the potato mixture evenly over the top, smoothing with a spatula.

Bake and Finish

1. Place dish on a baking sheet to catch drips.
2. Bake uncovered for 25–30 minutes, until the filling is bubbly and the top is golden.
3. For extra browning, broil for 2–3 minutes, watching closely.

Serve

1. Let the pie rest for 5–10 minutes before serving so the layers can set.
2. Serve warm with crusty bread or a crisp salad.