Heat oven to 375°F. Lightly grease a 9×13-inch baking dish.
Cover potatoes with cold water in a large pot. Bring to a boil and cook until tender, 15–18 minutes.
Warm olive oil in a skillet over medium heat. Soften onion for 4–5 minutes, then stir in garlic for 30 seconds. Cool slightly.
Stir breadcrumbs with 1/2 cup milk in a large bowl. Let stand 2 minutes to hydrate.
Add beef, sautéed onion and garlic, Worcestershire, 1/3 cup ketchup, 1 tsp salt, 1/2 tsp pepper, and paprika. Gently mix to combine.
Press meat mixture evenly into the baking dish. Brush with remaining ketchup. Bake 20–25 minutes until mostly set.
Drain potatoes well. Mash with butter, sour cream, 1/3 cup milk, 1 tsp salt, and 1/2 tsp pepper until creamy.
Spread mashed potatoes over the par-baked meatloaf. Rough up the top with a fork and sprinkle cheddar over.
Return to oven for 15–20 minutes, until bubbly and golden at the edges. Rest 10 minutes, then garnish with parsley and serve.