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 meat, bread crumbs, 1⁄3 cup ketchup, milk, onion, egg, garlic, and 1 teaspoon salt. Divide mixture into 4 equal portions. Shape each portion into a 4x2½-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.
In a large bowl, toss together green beans, sliced garlic, remaining 1 tablespoon oil, remaining 2 tablespoons vinegar, and remaining 1⁄2 teaspoon salt. Placeon other side of baking pan. Bake for 10 minutes more.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/cheesy-meatloaces-potatoes-green-beans/