Heat oil in a small sauté pan over medium-low heat. Add onion and sweat 5 minutes; add garlic and continue to sweat 5 more minutes. Remove from heat; let cool.
Gently mix ground chuck, eggs, carrot, breadcrumbs, milk, parsley, Worcestershire, salt, pepper, red pepper flakes and onion mixture in a large bowl until well combined; do not overmix. Stir ketchup and brown sugar in a small bowl.
Form meatloaf mixture into an 8 x 4-inch loaf on parchment paper-lined half sheet tray; evenly brush top with ketchup mixture. Place meatloaf on middle rack in oven; place small pan of water on rack underneath meatloaf in oven. Bake at 325°F for 1 hour 15 minutes or until internal temperature reaches 160°F. Let meatloaf rest 15 minutes; cut into ½-inch-thick slices.
Warm ½ tablespoon oil on the griddle or in a sauté pan over medium heat. Add the meatloaf and cook 5 minutes or until heated through. Cook 1 egg in ½ tablespoon oil in a skillet sunny-side up or to desired doneness.
Toast 2 pieces of Texas toast. Top 1 piece of toast with 2 pieces lettuce, 2 slices tomato, 4 pieces bacon, meatloaf, fried egg and 1 piece toast. Serve with spicy mayonnaise on the side.