Place the peeled and cubed potatoes in a large pot of salted water. Bring to a boil and cook for 15–20 minutes, until tender. Drain, then mash with butter and milk. Season with salt and pepper, and stir in half of the cheddar cheese.

While the potatoes cook, heat a skillet over medium-high heat. Add ground meat, breaking up with a spoon until browned. Drain excess fat.

Stir in onion and carrots; sauté 5 minutes until softened. Sprinkle in flour, stirring to coat. Add tomato paste, beef broth, and Worcestershire sauce. Simmer 3–4 minutes until thickened, then fold in peas. Season with salt and pepper.

Preheat oven to 400°F (200°C). Spoon the meat mixture into a baking dish. Spread mashed potatoes on top, creating peaks with a fork. Sprinkle remaining cheddar cheese over the potatoes.

Bake for 20–25 minutes until the topping is golden brown and bubbly. Let rest 5 minutes before serving.