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1
Preheat oven to 350. Place a large saute pan over medium-high heat and add 1/4 cup of the olive oil or herb oil. When it begins to shimmer, add half of the shallots and cook, stirring occasionally, until translucent. Add mushrooms and toss to coat, then cook until they begin to color but are still plump, approximately 12 to 15 minutes. Add white wine to deglaze pan and allow to cook down into a syrup, approximately 5 to 7 minutes. Put the mushrooms into a large bowl and reserve.
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2
Meanwhile, in another bowl, toss the radicchio with 1/4 cup olive oil or herb oil and season with salt and pepper. Spread the strips out onto a baking pan and place in the oven until the strips are lightly browned around the edges, approximately 15 minutes. Combine with mushrooms and reserve.
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3
Make the bechamel. Place a saucepan over medium heat and melt the butter. When it foams, add the rest of the shallots and cook until translucent. Add the garlic and stir to combine, then cook until the garlic has started to soften. Sprinkle flour over the top and stir to combine, then cook gently until the mixture has turned light brown and gives off a nutty scent, approximately 10 minutes. Add milk to the mixture, whisking all the while, until the sauce is thick. Add the nutmeg and 1/4 cup of grated Gruyere and 1/4 cup of grated Fontina, then stir to combine. Season to taste with salt and pepper.
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4
Reserve a cup of bechamel. Pour the rest over the mixture of mushrooms and radicchio, and stir.
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5
Assemble lasagna. Spread plain bechamel across the bottom of a 9- by-13-inch baking pan. Place a layer of lasagna sheets across the sauce, being careful not to overlap. Spread a generous layer of mushroom mixture on top of the pasta, and follow with some grated Fontina and Gruyere. Put another layer of pasta above the cheese, and top with smoked mozzarella. Repeat until the pasta is gone and the pan is full. Top with remaining cheeses and a generous amount of grated Parmesan.
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6
Bake 45 min., then brown top.
