To Make Onion Béchamel:

1. Melt butter in large saucepan over low.
2. Add flour, and slowly whisk until it resembles wet sand. Cook over low, whisking constantly, until mixture is shiny and smells toasty, about 2 minutes.
3. Whisking constantly, gradually add cold milk. Once fully combined, switch to a wooden spoon.
4. Add onion half, salt, and nutmeg. Cook over low to medium-low at a very gentle simmer, stirring very often, until onion is cooked through and sauce is very thick, about 45 minutes.
5. Pour through a fine wire-mesh strainer; discard solids. Use warm, or refrigerate in airtight container; reheat slowly over low heat, adding a splash of water to loosen, if needed.

To Make Mushroom Ragú:

1. Pour 3 cups cold water over dried porcini in a medium bowl; let soak 30 minutes. While porcini soak, wipe wild mushrooms with a damp paper towel to remove grit. Coarsely chop wild mushrooms. Strain porcini, reserving soaking liquid. Set aside.
2. Melt 2 tablespoons butter in a large skillet over medium-low. Add onion, garlic, ½ teaspoon sea salt, and ¼ teaspoon black pepper; cook, stirring occasionally, until softened, about 10 minutes.
3. Add wild mushrooms, remaining 1 tablespoon butter, and remaining 1 teaspoon sea salt. Increase heat to medium-high; cook, stirring occasionally, until softened, about 5 minutes. 
4. Add strained porcini and remaining ¼ teaspoon black pepper, and stir to combine. 
5. Add wine; cook, stirring often, until wine is reduced by half, about 3 minutes. 
6. Add porcini soaking liquid and Parmesan rind. Gently simmer over medium-high, stirring occasionally, until mushrooms are tender and liquid is mostly reduced, about 20 minutes. 
7. Taste and adjust seasoning as needed. Remove from heat; let cool 5 minutes. Remove Parmesan rind. Stir in chopped parsley.

To Make Lasagna: 

1. Cook the pasta according to package instructions for al dente. Remove from water using kitchen tongs, and submerge in ice water 30 seconds. Remove from ice water, and lay flat on kitchen towels. (Do not stack.) Smooth out pasta using your hands. Repeat with remaining pasta strips.
2. Preheat oven to 375°F. Grease inside of a deep 13- x 9-inch baking dish with butter. Spread ¾ cup béchamel on bottom of prepared dish.
3. Top with strips of pasta, covering bottom of dish completely. Spread with 1 cup béchamel; top with 1 ⅔ cups ragù. Sprinkle with ⅓ cup grated Parmesan. Top with strips of pasta. Spread with 1 cup béchamel. Top evenly with half of prosciutto. Sprinkle with 1 ⅓ cups fontina and ⅓ cup grated Parmesan.
4. Repeat step above until you run out of ingredients. Spread with remaining béchamel, and sprinkle with remaining fontina and remaining Parmesan.
5. Cover lasagna with aluminum foil. Bake on a rimmed baking sheet on middle rack in preheated oven 55 minutes. Remove foil; bake until top is golden brown, about 35 minutes. Remove from oven; let rest at least 30 minutes before serving. Serve warm, paired with fresh, crusty bread and a crisp side salad for a complete and comforting meal.