FOR THE CHEESE SAUCE: Whisk all ingredients in bowl until well combined; set aside.
FOR THE TOMATO SAUCE: Heat oil in large saucepan over medium heat. Add onion, sugar, pepper flakes, oregano and salt and cook, stirring frequently, until onions are softened, about 10 minutes. Add garlic and anchovies and cook until fragrant, about 2 minutes. Stir in crushed tomatoes, diced tomatoes, cheese and tomato paste; bring to simmer. Reduce heat to medium-low and simmer until slightly thickened, about 20 minutes.
FOR THE LASAGNA: While sauce simmers, lay noodles in 9 by 13-inch baking dish and cover with boiling water. Let noodles soak until pliable, about 15 minutes, separating noodles with tip of paring knife to prevent sticking. Place dish in sink, pour off water and run cold water over noodles. Pat noodles dry with clean dish towel; dry dish. Cut two noodles in half crosswise (short side).
Adjust oven rack to middle position and heat oven to 375 degrees. Spread 1 1/2 cups tomato sauce in bottom of dish. Lay 3 noodles lengthwise in dish with ends touching 1 short side of the pan, leaving space on opposite short side. Lay 1 half noodle crosswise in empty space to create even layer of noodles. Spread half of cheese sauce over noodles, followed by 1/2 cup fontina. Repeat layering of noodles, alternating which short side gets half noodle (alternating sides will prevent lasagna from buckling). Spread 1 1/2 cups tomato sauce over second layer of noodles, followed by 1/2 cup fontina. Create third layer using 3 1/2 noodles (reversing arrangement again), remaining cheese sauce, and 1/2 cup fontina.
Lay remaining 3 1/2 noodles over cheese sauce. Spread remaining tomato sauce over noodles. Toss remaining 1/2 cup fontina with 1/8 teaspoon cornstarch, then sprinkle over tomato sauce, followed by Pecorino.
Spray sheet of aluminum foil with vegetable oil spray and cover lasagna. Bake for 35 minutes. Remove lasagna from oven and increase oven temperature to 500 degrees.
Remove foil from lasagna, return to oven, and continue to bake until top is lightly browned, 10 to 15 minutes longer. Let lasagna cool for 20 minutes. Sprinkle with basil, cut into pieces, and serve.