Preheat oven to 375 degrees. Pulse bread in a food processor until finely ground. (You should have about 2 1/2 cups breadcrumbs.) Transfer to a medium bowl.
Pulse garlic, onion, celery, carrot, and parsley in food processor until finely chopped. Add to breadcrumbs. Add meats, egg, 1/4 cup ketchup, the mustard, Worcestershire sauce, 1 tablespoon salt, and 1/2 teaspoon pepper; mix together using your hands. Transfer mixture to a 5-by-9-inch loaf pan.
Stir together remaining 1/2 cup ketchup and the brown sugar until smooth; brush onto meat. Set pan on a rimmed baking sheet, and bake until an instant-read thermometer inserted into the center reaches 160 degrees, about 1 hour 20 minutes. Let cool slightly.