Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x5-inch loaf pan.
Combine beef, egg, onion, milk, bread crumbs, parsley, and carrot in a large bowl. Season with salt and black pepper. Place beef mixture in loaf pan.
Stir together brown sugar, mustard, and ketchup in a small bowl. Pour over meatloaf.
Bake in preheated oven until no longer pink in the center, about 1 hour. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C).
