Heat oven to 425°F. In a large glass bowl, prepare scalloped potatoes for baking (using 2 cups boiling water, 1/2 cup milk, and 2 tablespoons butter). Place bowl in microwave and cook 5 minutes; stir and cook 5 minutes more. Set aside. In a medium bowl, microwave carrots and 1 tablespoon water, covered, for 5 minutes.
In a 1-1/2- or 2-quart baking dish, stir together beef, cooked carrots, drained tomatoes, and vinegar. Spoon potato mixture over beef mixture, and sprinkle with bread crumbs. Spray top with vegetable cooking spray. Bake 15 to 20 minutes, until hot and bubbly.