Place the peeled and quartered potatoes in a large pot and cover with cold, salted water. Bring to a boil and cook until fork-tender, about 15-20 minutes. While the potatoes cook, start the meat filling.

Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the ground beef (or lamb) and cook, breaking it up with a spoon, until deeply browned and no pink remains. Drain any excess grease and set the meat aside, leaving about 1 tbsp of fat in the pan.

Reduce the heat to medium. Add the diced onion, carrots, and celery to the pan. Sauté gently, stirring occasionally, until the vegetables soften—about 7 to 10 minutes. Stir in the minced garlic and tomato paste and cook for 1 minute until fragrant.

Sprinkle the flour over the vegetables and stir until everything is coated. Cook for 1 minute. This is called a roux, and it ensures a smooth, thick gravy. Now, pour in the red wine (if using) and scrape up any brown bits stuck to the bottom of the pan—this is crucial for flavor! Let the wine reduce by half.

Stir the meat back into the pan. Add the beef stock, Worcestershire sauce, thyme, and rosemary. Bring the mixture to a gentle simmer. Reduce the heat to low and let it cook uncovered for about 10-15 minutes, allowing the sauce to thicken slightly and the flavors to meld. Season generously with salt and pepper.

Stir in the frozen peas and corn. Scoop the filling into a 9x13 inch casserole dish or a cast iron skillet. Spread evenly.

Drain the cooked potatoes completely and return them to the empty pot. Add the softened butter, warm milk, and cream cheese (if using). Mash until very smooth. Stir in the egg yolk and season with salt and pepper. The yolk ensures the topping browns beautifully and creates a stable crust, preventing the potatoes from sinking into the filling.

Gently spoon the mashed potatoes over the meat filling, starting in the middle and working your way out. Use a fork to create little peaks, which crisp up nicely in the oven. If desired, sprinkle the top with a layer of sharp cheddar cheese.

Bake in a preheated oven at 375°F (190°C) for 25-30 minutes, or until the filling is bubbling hot and the mashed potato crust is golden brown. Let it rest for 10 minutes before serving. This rest allows the filling to set up, preventing a messy scoop.