In a large bowl, toss together potatoes, 1 tablespoon oil, and 1 teaspoon salt. Spoon onto one side of an 18x13-inch rimmed baking sheet.
In a large bowl, combine beef, bread crumbs, 1⁄3 cup ketchup, milk, onion, egg, minced garlic, and 1 teaspoon salt. Divide mixture into 4 portions. Shape each portion into a 4x2 1⁄2-inch loaf. Place 1 stick of cheese in center of each loaf, and shape mixture around cheese. Place loaves in center of pan.
In a small bowl, combine brown sugar, 2 tablespoons vinegar, and remaining 3⁄4 cup ketchup. Spoon over loaves.
Bake for 15 minutes. Leave oven on.
In a large bowl, toss together green beans, sliced garlic, remaining 2 tablespoons vinegar, remaining 1 tablespoon oil, and remaining 1⁄2 teaspoon salt. Place on other side of pan.
Bake for 10 minutes.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/cheesy-meatloaves-potatoes-green-beans/