Heat oven to 375°F. Place bread in the bowl of a food processor fitted with the steel blade; pulse until fine crumbs form. Transfer to a medium bowl, and add ground beef.
Place onion, garlic, celery, carrots, and parsley in the bowl of a food processor fitted with the steel blade; pulse until fine. Add to meat mixture, using hands to mix well.
Add egg, ½ cup ketchup, 2 teaspoons dry mustard, salt, and pepper; use hands to combine thoroughly. Place in an 8 ½-by-4 ½-by-2 ½-inch loaf pan.
Combine remaining ½ cup ketchup, remaining teaspoon dry mustard, and brown sugar in a bowl; stir until smooth. Brush mixture over meatloaf.
Place in the oven with a baking pan set on the rack below to catch drippings. Cook until a meat thermometer inserted in the center reads 160 degrees, about 90 minutes.
