Begin by preheating your oven to 375°F. and mixing the cheeses with seasonings to create a rich, flavorful filling. Layer the lasagna noodles with the cheese mixture and sauce, then bake until golden and bubbly.
If you're using traditional noodles, cook them according to the package instructions until al dente, then drain and set aside. For no-boil noodles, you can skip this step.
In a large bowl, combine the ricotta, mascarpone, half of the grated Parmesan cheese (save the rest for topping), salt, pepper, and the beaten egg. Stir in the torn basil leaves. This is your cheese mixture.
Spread a thin layer of red sauce on the bottom of a 9x13-inch baking dish. This will prevent the noodles from sticking and give the first layer of pasta something to cozy up to.
Place a layer of lasagna noodles over the sauce. Then, spread a portion of the cheese mixture over the noodles, followed by a sprinkle of shredded mozzarella and fontina. Drizzle some more red sauce over the cheese.
Repeat the layering process (noodles, cheese mixture, mozzarella, fontina, sauce) until all ingredients are used, finishing with a layer of noodles topped with the remaining red sauce, mozzarella, fontina, and the reserved grated Parmigiano Reggiano.
Cover the baking dish with aluminum foil, being careful not to let it touch the cheese to prevent sticking. Bake in the preheated oven for 25 minutes.
After 25 minutes, remove the foil and continue to bake for an additional 15-20 minutes, or until the cheese is bubbly and starting to brown. If you like a crispy top, you can broil for the last few minutes—just keep an eye on it to prevent burning.
Let the lasagna rest for about 10 minutes before slicing. This allows the layers to be set, making it easier to serve.