Instructions

FOR THE SAUCE: Bring 4 quarts water to boil in large pot. Fill large bowl halfway with ice and water. Add spinach and 1 tablespoon salt to boiling water and cook, stirring often, until spinach is just wilted, about 5 seconds. Using slotted spoon, transfer spinach to ice bath and soak until completely cool, about 1 minute; drain spinach and transfer to clean dish towel. Wrap towel tightly around spinach to form ball and wring until dry. Chop spinach and set aside.
Melt butter in medium saucepan over medium heat. Add shallots and garlic and cook, stirring frequently, until shallots are softened, about 4 minutes. Add flour and cook, stirring constantly, until thoroughly combined, about 1 ½  minutes; mixture should not brown. Gradually whisk in milk; increase heat to medium-high and bring to boil, whisking often. Stir in bay leaves, nutmeg, ½  teaspoon salt, and ¼  teaspoon pepper; reduce heat to low; and simmer, whisking occasionally, for 10 minutes. Discard bay leaves, then whisk in ½  cup Parmesan until completely melted. Reserve ½  cup sauce in small bowl; press plastic wrap directly against surface and set aside. Transfer remaining sauce to second bowl and stir in spinach, mixing well to break up any clumps; press plastic directly against surface and set aside.
FOR THE CHEESE FILLING: Process cottage cheese, egg, and salt in food processor until very smooth, about 30 seconds.
Adjust oven rack to middle position and heat oven to 425 degrees. Pour 2 inches boiling water into 13 by 9-inch broiler-safe baking dish. Slip noodles into water, one at a time, and soak until pliable, about 5 minutes, separating noodles with tip of paring knife to prevent sticking. Remove noodles from water and place in single layer on clean dish towels; discard water. Dry and grease dish.
Spread reserved sauce evenly over bottom of prepared dish. Arrange 3 noodles in single layer on top of sauce. Spread 1 cup spinach mixture evenly over noodles, sprinkle remaining 1 cup Parmesan over spinach mixture, and top cheese with 3 noodles. Spread 1 cup spinach mixture evenly over noodles, sprinkle 1 cup fontina over spinach mixture, and top with 3 noodles. Spread 1 cup spinach mixture evenly over noodles, followed by cheese filling. For final layer, arrange remaining 3 noodles over cheese filling, then cover noodles with remaining spinach mixture. Sprinkle remaining 1 cup fontina over spinach mixture.
Cover dish tightly with aluminum foil that has been sprayed with vegetable oil spray and bake until edges are just bubbling, about 20 minutes, rotating dish halfway through baking. Remove dish from oven and remove foil. Adjust oven rack 6 inches from broiler element and heat broiler. Broil lasagna until cheese on top becomes spotty brown, 4 to 6 minutes. Let lasagna cool for 15 minutes before serving.