Cover potato chunks with cold salted water, bring to a boil, and cook 15–18 minutes until fork-tender. Drain, return to the pot, and let steam 1 minute. Mash with butter, then add warm milk, sour cream, salt, and pepper. Mash until thick and smooth. Cover and set aside. Preheat oven to 400°F.
Heat olive oil in a large oven-safe skillet over medium-high heat. Add ground beef and let sit 1–2 minutes before breaking up. Cook 6–7 minutes until well browned. Drain most fat, leaving about 1 tablespoon.
Add onion and carrots; cook 4–5 minutes until softened. Add garlic; cook 30 seconds. Add tomato paste and cook, stirring, for 1 full minute until slightly darkened. Add Worcestershire sauce and flour; stir to coat. Pour in beef broth, add thyme, rosemary, bay leaf, salt, and pepper. Simmer 5–8 minutes until gravy coats the back of a spoon. Remove bay leaf. Fold in frozen peas.
Spoon mashed potatoes in large dollops over the filling, then spread to the edges. Create ridges on the surface with a fork. Sprinkle cheddar on top if using.
Bake 20–25 minutes until the top is golden and the filling bubbles at the edges. For deeper browning, broil 2–3 minutes. Rest 5–10 minutes before serving.