Preheat oven to 325°F.
Cover potatoes with water and bring to a boil. Salt water and boil to tender. Drain and return to hot pot, mash with milk and cheddar, and season with salt and pepper. Cover to keep warm.
Melt 1 tablespoon of butter in a small skillet over medium-high heat. Add brats and brown until crisp.
Mix half the brats into potatoes and reserve the rest to top the potatoes before serving.
Season the chops or chicken aggressively with salt and pepper. Heat oil in a large skillet over medium high heat. Add meat and brown on each side, transfer to oven to finish cooking through, 12-15 minutes.