Preheat oven to 375°F (190°C).
Boil potatoes in salted water until fork-tender, about 15–20 minutes.
Drain potatoes and mash with butter, milk, salt, pepper, and cheddar cheese until smooth.
Meanwhile, cook ground beef in a large skillet over medium heat until browned.
Add onion, bell pepper, and garlic. Cook until vegetables soften.
Stir in tomato sauce, tomato paste, ketchup, Worcestershire sauce, brown sugar, mustard, paprika, salt, and pepper.
Simmer for 10 minutes until the mixture thickens.
Transfer the beef mixture to a greased 9x13-inch baking dish.
Spread the mashed potatoes evenly over the beef layer.
Top with additional cheddar cheese if desired.
Bake for 20–25 minutes until heated through and lightly golden.
Allow to rest for 5 minutes before serving. Garnish with parsley.