Nonna's Meatball Sandwich

Prepare the meatballs: Combine the breadcrumbs and milk in a small bowl and set aside for 5 minutes. Drain in a wire sieve and press out the milk. Crumble the bread into a large bowl. Add the ground chuck, sausage, onion, garlic, Parmigiano-Reggiano cheese, parsley, egg, salt and pepper and mix with clean hands until combined. Using hands rinsed under cold water, shape into 16 meatballs and transfer to a baking sheet. Refrigerate while making the sauce to firm them up.

Make the tomato gravy: Pour the oil into a large Dutch oven and add the onion and garlic. Place over medium heat and cook, stirring often, until the onion is golden, 5 to 7 minutes. Take your time with this, as you do not want to brown the garlic; starting the cooking in a cold pot will help. Stir in the tomatoes. Fill the can with water and stir the water into the sauce. This will dilute the sauce but also allow you to simmer for longer as it reduces and gains flavor. Add the basil and sugar and cover. Increase the heat to high and bring to a boil, stirring often.

Reduce the heat to medium so the sauce is gently boiling. Season to taste with salt and pepper. One at a time, reshape the meatballs and drop them into the sauce. Adjust the heat so the sauce is simmering. Cook, uncovered, without stirring, until the meatballs have set, 10 to 15 minutes. Give them a gentle stir. Reduce the heat to medium-low so the sauce is cooking at a low simmer. Cook, uncovered, stirring occasionally, until the sauce reduces by about one-third and turns deep red with some oily patches, 2 to 2½ hours. Using a slotted spoon, transfer the meatballs to a bowl.

Arrange a broiler rack about 4 inches from the source of heat and preheat on high.

Arrange the rolls, cut sides up, on a baking sheet. Top the bottom half of each roll with three slices of mozzarella cheese. Broil until the cheese is melted, 1 to 2 minutes. Add four meatballs on top of the cheese and cut each meatball in half with the side of the spoon (this helps make the sandwich more compact). Spoon about ¼ cup of the sauce on top. Sprinkle with 2 tablespoons of Parmigiano-Reggiano cheese. Close the roll, cut the sandwich in half and serve with the warm remaining sauce on the side. (The leftover sauce can be cooled, covered and refrigerated for up to three days or frozen for up to six months.)