For the sauce: Heat 2 tablespoons olive oil in a large skillet set over medium heat. Add the minced garlic and onions and saute until the onions are translucent, about 5 minutes. Remove the mixture from the heat and let cool. Transfer the mixture to a blender and add the tomato puree. Blend until smooth.
Heat the remaining 2 tablespoons olive oil in a medium pot set over medium heat. Add the sliced garlic and cook until the garlic is golden brown, about 30 seconds. Remove the garlic with a slotted spoon, leaving the oil in the pot. Carefully pour the tomato sauce into the pot, reduce the heat to medium-low and let simmer while you prepare the meatballs.
For the meatballs: In same skillet, heat 2 tablespoons olive oil over medium heat and add the garlic and onions. Saute 5 minutes, and then remove from the heat to cool.
In a bowl, combine the milk and breadcrumbs and stir until the crumbs look like wet sand. Add a little more milk if it looks too dry.
In a large bowl, combine the ground meats, sausage, parsley, basil, eggs, some salt and pepper, the cooked onion-garlic mixture and the breadcrumbs. Stir with your hands until just mixed, and then form 24 small meatballs. Place the meatballs on a baking sheet or plate.
Reheat the large skillet over medium-high heat and add the remaining 2 tablespoons olive oil. When the oil is hot, add half the meatballs and cook until browned on all sides, turning a few times during cooking, about 5 minutes. Repeat with the remaining meatballs. Transfer all the meatballs to the simmering tomato sauce and cook for a few minutes, until cooked through.
To serve, place 2 meatballs on each slider roll and spoon some sauce on top. Top the meatballs with a slice of cheese and serve. You may have leftover sauce.
This recipe was created by a contestant during a cooking competition. The Food Network Kitchens have not tested it for home use, therefore, we cannot make any representation as to the results.