This lasagna was designed for a deep-dish baking pan. You can use a standard nine-by-thirteen-inch baking pan, but you will have extra sauce. The recipe can be assembled a day ahead and left to cool.
Pass tomatoes through a food mill fitted with the large disc; set aside. Heat oil in a medium skillet over medium-low heat. Add garlic; cook until soft and light golden brown, about 2 minutes. Add reserved tomatoes, and simmer until thickened, about 35 minutes. Season with 2 teaspoons salt and 1 teaspoon pepper. Stir in torn basil leaves; set aside.
In a large bowl, combine ricotta and Parmesan cheeses, butter, nutmeg, 1 teaspoon salt, and 1/2 teaspoon pepper. Stir until well combined. Set aside.
Oil a rimmed baking sheet; set aside. Cover and bring a large pot of salted water to a boil. Add one sheet of pasta at a time to boiling water. Cook for 1 minute, and transfer to prepared baking sheet. Repeat until all pasta has been cooked.
Preheat oven to 350 degrees. Line a baking sheet with a Silpat or parchment paper; set aside. Assemble the lasagna: Spread 1/2 cup tomato sauce in the bottom of a 9-by-13-inch baking pan. Place a layer of lasagna sheets in the pan, allowing sheets to hang over the ends of pan. Spread 1/4 of the ricotta-cheese mixture evenly over pasta and sprinkle with mozzarella. Top with a layer of pasta, cut to fit inside pan. Spread 1 cup tomato sauce over pasta. Repeat layering process, alternating pasta layers with cheese and sauce layers (there should be a total of three cheese layers and two sauce layers).
Bring pasta hanging over ends of the pan up and over the top of final layer. Use more pasta, if necessary, to completely cover top. Spread with 1 1/2 to 2 cups tomato sauce. Dollop top of lasagna with remaining ricotta cheese mixture. Sprinkle with remaining mozzarella. Place on prepared baking sheet, and transfer to oven. Bake until the top is bubbling and light golden brown, 45 to 50 minutes; garnish with whole basil leaves.
Cover, unbaked, and refrigerate up to one day in advance, or freeze, unbaked, up to three weeks in advance. Defrost it overnight in the refrigerator; bake as directed.