For the sauce, heat a large Dutch oven over medium heat, and add the olive oil. When the oil is hot, add the garlic and let sizzle until just golden, about 1 minute. Add a pinch of peperoncino and the crushed tomatoes. Rinse out the cans with 2 cups water, and add that as well. Season with salt, and put the basil sprigs in the sauce. Simmer until flavorful and slightly thickened, about 20 minutes. Discard the basil sprigs, and add the cream. Simmer just until the sauce comes together, 3 to 4 minutes. Season again with salt and peperoncino. You should have 6 to 7 cups of sauce.

To assemble the lasagna, preheat the oven to 400 degrees. Spread about a cup of sauce in the bottom of a 9-by-13-inch baking dish. Cover the sauce with three noodles (there will be extra space around the noodles, and that’s okay— they will expand as they absorb the sauce). Spread another cup of sauce over the noodles, then sprinkle with 1 cup mozzarella and ½ cup Grana Padano. Top with another layer of noodles. Continue with sauce, mozzarella, and Grana Padano, layering in the same manner, until you add the fifth layer of noodles. Top that layer just with sauce and grated Grana Padano (not mozzarella).

Tent the lasagna with foil, and place on a baking sheet to catch any drips. Bake until the edges are bubbling, about 30 to 35 minutes. Uncover the lasagna, and bake until the top is browned and crusty, about 20 to 30 minutes more. Let the lasagna rest out of the oven for at least 30 minutes before slicing and serving.