Combine applesauce, egg, bread crumbs, and salt and pepper, with ground beef; mix until well blended. (This is best done by hand.) Form mixture into medium-sized meatballs, and roll in flour.
Heat 1 teaspoon of oil in a large skillet over medium high or high heat. Cook meatballs, turning occasionally, until evenly browned but not cooked through. Transfer to a baking dish and set aside.
In the same skillet, partially cook the carrots and onions over medium high heat. Add tomato juice, season to taste with salt and pepper, and bring to a boil. Reduce heat, and simmer for 5 minutes, then pour over meatballs.
Cook, covered, in the preheated oven for 45 minutes, or until carrots are tender and meatballs are cooked through. Cook uncovered for 10 minutes before removing from the oven.