Preheat the oven to 400°F. Butter a 9-by-13-inch baking dish.

In a small bowl, combine the pesto sauce and the ricotta cheese. Mix well. Set aside.

To make the béchamel: In a small saucepan, heat the milk over medium-low heat until bubbles form around the edges of the pan. In another medium saucepan, melt the butter over medium heat. Gradually whisk in the flour and continue whisking for about 3 minutes or until the mixture turns a golden color. Gradually whisk the hot milk into the mixture until smooth. Continue to whisk until the mixture thickens. Add salt and pepper. Cover and remove from heat.

In a large pot of boiling salted water, cook the pasta for about 8 minutes, or until al dente. Drain. Meanwhile, mix the 2 cheeses together well. Put a layer of lasagne in the dish, then spread the pesto mixture on top. Add another layer of lasagne and top with the mushrooms. Ladle a thin layer of béchamel over the mushrooms, then sprinkle half of the mixed cheeses over the sauce. Put another layer of lasagne on top and ladle on more béchamel sauce, spreading it to completely cover the pasta (you don't have to use up all the sauce). Sprinkle the top with the remaining cheese and the hazelnuts. Bake for 20 minutes, or until the cheese has melted and browned slightly. Remove from the oven and let sit for 5 to 10 minutes before cutting into squares to serve.

Note: Toasting and skinning hazelnuts: Preheat the oven to 350°F Spread the hazelnuts in a rimmed baking sheet. Toast in the oven until fragrant, about 8 minutes. Wrap in a clean kitchen towel and rub with the towel to remove most of the skins.