Boil potatoes in salted water 15–20 minutes until tender. Heat 6 tbsp butter and milk together until butter melts. Drain potatoes, mash until smooth, blend in the hot butter mixture, and stir in cheddar. Season with salt and pepper. Cover and set aside.
Heat oven to 375°F. Melt remaining 2 tbsp butter in a large oven-safe skillet over medium heat. Add onion, carrot, garlic, thyme, and rosemary; cook until onions are translucent and carrots just tender, about 10 minutes. Add beef, lamb, and mustard powder; cook, breaking up the meat, until no longer pink. Drain excess fat if desired.
Add tomato paste and stir 2–3 minutes. Add flour and cook 1 minute. Add beef stock and Worcestershire and cook until slightly thickened. Stir in peas and parsley, remove herb stems, and season.
Top the meat mixture with dollops of mashed potato, then spread into an even layer. Bake until potatoes are beginning to brown and edges are bubbling, about 30 minutes. Rest 15 minutes before serving.