Make the sauce: In a medium skillet, heat the olive oil over medium heat. Add the onion and garlic and season with 1 tablespoon salt. Stir in the red pepper flakes and sugar, and cook for about 2 minutes. Then add the tomatoes, with their juices, and the oregano. Cook for a few minutes over high heat, stirring from time to time. Taste for seasoning, add the basil leaves, and remove from the heat.
Make the meatballs: Put the beef and veal in a large bowl and spread the meat all over the bottom of the bowl and up the sides a little. (This will help you to distribute the seasonings evenly through the meat.) Sprinkle with 2 teaspoons salt. Then sprinkle the bread crumbs, Parmigiano-Reggiano, and parsley all over the meat and use your hands to mix the ingredients together. In a small bowl, whisk together the egg and garlic. Drizzle the egg mixture over the meat. Mix the meat thoroughly with your hands.
Test a meatball: Form 1 small meatball (about 1 inch in diameter) with your hands. Heat a splash of the canola oil in a small skillet over high heat. When the oil begins to smoke lightly, add the meatball, lower the heat, and cook it over medium heat for 2 to 3 minutes. Taste for seasoning and texture. If it seems too wet, add some more bread crumbs to the mixture in the bowl. If it is too dry, add a splash of water. Adjust the seasoning of the mixture in the bowl as needed. Roll the remaining meat into balls; you should have about 40 very small meatballs.
Cook the meatballs: Heat a large skillet over medium heat and add half of the remaining canola oil. When the oil begins to smoke lightly, remove the pan from the heat and add half of the meatballs in a single layer, spreading them apart somewhat so they have a chance to brown instead of steaming. Return the pan to high heat and brown the meatballs, turning them so they brown all around, until medium-rare, 2 to 3 minutes. Use a slotted spoon or spatula to transfer them to a baking sheet lined with a kitchen towel to drain. Wipe out the skillet and repeat the process with the remaining canola oil and meatballs.
Cook the pasta: Bring 6 quarts water to a rolling boil in a large pot over high heat and season with 1/2 cup salt. The pasta water should taste like seawater. Add the lasagna sheets, stirring with a slotted spoon to make sure they do not clump or stick to the bottom, and cook for 4 minutes. Drain in a colander, rinse under cold water, and drain again. The pasta should still be very firm to the touch. Separate the sheets carefully so they don't stick together.
Preheat the oven to 350 degrees F.
Assemble the lasagna: Spoon a thin layer of the sauce over the bottom of a 9 x 13-inch baking pan. Arrange a layer of pasta sheets over the sauce. Sprinkle one-fourth of the mozzarella, ricotta, and Parmigiano-Reggiano over the pasta, and then add another thin layer of sauce. Dot the surface with about one-third of the meatballs, spacing them evenly. Repeat the layering process two more times. Add a final layer of pasta and top it with the remaining sauce and cheese.
Bake the lasagna: Cover the dish tightly with foil and put it in the center of the oven. Bake for 45 minutes. Then raise the oven temperature to 450 degrees F and remove the foil. Bake the lasagna until the top browns slightly, 10 to 15 minutes. Remove the lasagna from the oven and allow it to cool for 15 minutes or so before serving.
"The Home Cook: Recipes to Know by Heart" by Alex Guarnaschelli © Clarkson Potter 2017. Provided courtesy of Alex Guarnaschelli. All rights reserved.