To make the glaze, combine ketchup, brown sugar, and vinegar. Set aside.
For the meat loaves, preheat the oven to 350 degrees F. Oil a foil-lined rimmed baking sheet.
Heat the oil in a medium skillet over medium heat. Add the celery, onion, and garlic and cook, stirring until the vegetables have softened, about 5 minutes. Transfer to a large bowl, stir in 1/4 cup of the glaze and let cool.
Add the sour cream, bread crumbs, egg, milk, parsley, mustard, salt, thyme, and pepper and stir until combined. Add the chuck, pork, and veal and combine well. (To taste for seasoning, fry a pinch of the meat mixture in a small skillet over medium-high heat until browned and cooked through, about 5 minutes. Season with additional salt and pepper, if needed.)
Scoop mixture onto baking sheet using 1/2 cup measure. Shape into ovals.
Divide the remaining glaze over the tops of the loaves. Bake 35 to 40 minutes. The internal temperature should be 165 degrees F when tested with an instant-read thermometer. Serve at once, while warm.
The meat loaves can be prepared in advance and kept frozen until just before baking. Wrap the loaves with plastic wrap, then slip into resealable plastic bags. Increase the cooking time by about 10 minutes for frozen meat loaves.
Recipe courtesy of Sara Moulton, Sara Moulton Cooks at Home, Broadway Books, 2002