Be sure to use Italian fontina rather than bland and rubbery Danish or American fontina; if it is not available, substitute whole milk mozzarella. To make the cheese easier to shred, freeze it for 30 minutes to firm it up. If fresh nutmeg is unavailable, use only 1/2 teaspoon ground nutmeg. Because the lasagna is broiled at the end of cooking to brown the surface, make sure to use a baking dish that is broiler safe.

Directions
For the Spinach
Fill large bowl with ice water. Bring 4 quarts water to boil in large Dutch oven or stockpot over high heat; add salt and spinach, stirring until spinach is just wilted, about 5 seconds. Using skimmer or fine-mesh strainer, transfer spinach to ice water and let stand until completely cool, about 1 minute, then drain spinach and transfer to clean kitchen towel. Wrap towel tightly around spinach to form ball and wring until dry. Chop spinach medium and set aside.

For the Béchamel
Melt 5 tablespoons butter until foaming in medium saucepan over medium heat; add shallots and garlic and cook, stirring frequently, until translucent, about 4 minutes. Add flour and cook, stirring constantly, for about 1 1/2 minutes; do not brown. Gradually whisk in milk. Bring mixture to boil over medium-high heat, whisk in bay leaves, nutmeg, salt, and pepper; reduce heat to low and simmer 10 minutes, whisking occasionally. Whisk in Parmesan and discard bay leaves. Transfer sauce to bowl, press plastic wrap directly against surface, and set aside.

For the Cheese, Pasta and Assembly
Blend cottage cheese, egg, and salt in food processor or blender until very smooth, about 30 seconds. Transfer to bowl and set aside. Adjust oven rack to middle position and heat oven to 425 degrees. Place noodles in 13 by 9-inch broiler safe baking dish and cover with hot tap water; let soak 5 minutes, agitating noodles occasionally to prevent sticking. Remove noodles from water and place in single layer on kitchen towel. Wipe baking dish dry and coat with remaining 1 tablespoon butter. Use rubber spatula to distribute 1/2 cup béchamel in bottom of baking dish; position 3 noodles on top of sauce. Stir spinach into remaining béchamel in bowl, mixing well to break up clumps of spinach (you should have about 4 cups spinach/béchamel mixture). Spread 1 cup spinach mixture evenly over noodles, sprinkle evenly with Parmesan, and top with 3 more noodles. Spread 1 cup spinach mixture evenly over noodles, sprinkle evenly with 1 cup fontina, and top with 3 more noodles. Spread 1 cup spinach mixture evenly over noodles, followed by cottage cheese mixture. Finish with 3 noodles, remaining cup spinach mixture, and remaining cup fontina. Lightly spray large sheet foil with nonstick cooking spray and cover lasagna. Bake until bubbling, about 20 minutes, then remove foil. Remove lasagna and adjust oven rack to uppermost position (about 6 inches from heating element) and heat broiler. Broil lasagna until cheese is spotty brown, 4 to 6 minutes. Cool 10 minutes, then cut into pieces and serve.