Heat oven to 375 degrees F.
Place bread in the bowl of a food processor fitted with a 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 a steel blade; pulse until fine. Add to meat mixture, using hands to mix well. Add egg, 1/2 cup ketchup, 2 teaspoons dry mustard, salt, and pepper; use hands to combine thoroughly. Place in an 8 1/2 by 4 1/2 by 2 1/2-inch loaf pan.
Combine remaining 1/2 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 F about 90 minutes. If top gets too dark, cover with foil, and continue baking.
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