Preheat the oven to 350 degrees F. Bring a large pot of salted water to a boil for the pasta. In a food processor, pulse 2 buns into coarse crumbs. Heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add the crumbs and toast 3 minutes. Transfer to a bowl. Wipe out the skillet.
Tear up the remaining bun; soak in a large bowl with the milk, 5 minutes. Drain, squeezing the excess milk from the bread. Combine the soaked bread, half of the toasted crumbs, the ground beef, onion, chopped pickles, 2 tablespoons ketchup, the mustard, Worcestershire sauce, 1/2 teaspoon salt and pepper to taste in the bowl and mix by hand.
Divide the meat mixture into 24 pieces. Press a cheese cube into the center of each and shape into meatballs around the cheese.
Heat the remaining 1 tablespoon olive oil in the same skillet over medium heat. Add the meatballs and cook until browned, about 2 minutes per side. Transfer the meatballs to a baking sheet; bake until just cooked through, about 5 minutes. Reserve the skillet.
Cook the pasta as the label directs. Meanwhile, add the garlic to the reserved skillet; cook over medium heat until golden, about 30 seconds. Add the tomato paste and the remaining 2 tablespoons ketchup; cook 1 minute, then stir in 1 cup pasta cooking water until smooth. Simmer until slightly thickened, about 3 minutes. Drain the pasta, add to the skillet and toss to coat. Divide the pasta among bowls and top with the remaining toasted breadcrumbs, the meatballs, grated cheddar, lettuce and tomato. Serve with pickle slices on the side.
Per serving (without toppings): Calories 541; Total Fat 19 grams; Saturated Fat 7 grams; Protein 30 grams; Total Carbohydrate 61 grams; Sugar: 8 grams; Fiber 3 grams; Cholesterol 66 milligrams; Sodium 680 milligrams;