Mix ground beef, milk, egg, cornmeal, onion, chili powder, and dry mustard together in a large bowl; divide and shape into meatballs.
Heat vegetable oil in a skillet over medium-high heat.
Spread 1/2 cup flour into a wide, shallow dish. Roll meatballs in flour to coat.
Cook coated meatballs in hot oil until browned on all sides, 5 to 7 minutes.
Remove meatballs from skillet with a slotted spoon to a casserole dish, reserving fat in the skillet. Arrange potato, carrots, and onion chunks atop the meatballs.
Stir 2 tablespoons flour into reserved fat until you have a smooth paste; add tomato juice and diced tomatoes. Bring the mixture to a simmer, reduce heat to medium-low, and cook, stirring occasionally, until slightly thickened, about 10 minutes; pour over the meatballs and vegetables. Place a cover on the casserole dish.
Bake in preheated oven until potatoes and carrots are completely tender, about 90 minutes.