Preparation

Make the sauce

• Heat the oil and garlic in a 4- to 5-quart pot over medium heat. Cook until the garlic is golden-brown, about 3 minutes. Discard the garlic. Add the tomatoes (careful—they spatter), the crushed red pepper, and 1 Tbs. salt; simmer gently, adjusting the heat as needed, until the tomatoes begin to break down, about 45 minutes. Whisk the tomatoes vigorously to break them up. Stir in the basil and let the sauce cool to room temperature. Season to taste with salt and crushed red pepper.

Assemble the lasagne

• Position a rack in the center of the oven and heat the oven to 350°F.
• Set aside 1-1/4 cups of the sauce and mix the remaining sauce with the ricotta in a medium bowl. Mix the mozzarella, fontina, and 1 cup of the Parmigiano in another medium bowl. 
• Spread 1/2 cup of the reserved tomato sauce on the bottom of a 9x13x3-inch baking dish. Cover the sauce with a slightly overlapping layer of cooked noodles, cutting them as needed to fill any gaps. Evenly spread 1-1/2 cups of the ricotta mixture over the noodles. Sprinkle 1 rounded cup of the grated cheese evenly over the ricotta. Add another layer of noodles, and repeat the layers as instructed above, to make a total of 4 ricotta-and-cheese layers and 5 pasta layers. Spread the remaining 3/4 cup plain sauce evenly over the top noodle layer. Sprinkle with the remaining 3/4 cup of Parmigiano-Reggiano. 
• Cover the baking dish with foil and bake for 40 minutes. Remove the foil and bake until the top is browned and bubbly, 15 to 20 minutes. Let cool for at least 10 minutes before serving.

Make Ahead Tips

You can assemble the lasagne up to 2 days ahead of baking it. Tightly wrap the baking dish in plastic and refrigerate it. Let the lasagne come to room temperature before baking it.

Sprinkle 1/4 cup crumbled cooked Italian sausage or browned ground beef and chopped onions over each layer of the ricotta mixture.

Or scatter 1/2 cup squeezed-dry, thawed frozen chopped spinach over each layer of the ricotta mixture.