In a heatproof glass measuring cup, cover dried porcini mushrooms with 1 cup of boiling water. Let stand until the mushrooms are soft, about 20 minutes. Drain and reserve 3/4 cup of the porcini soaking liquid. Finely chop the mushrooms.

Preheat the oven to 375 degrees. In a large pot of boiling salted water, cook the mixed pasta until just shy of al dente, about 10 minutes; drain.

Meanwhile, in a large saucepan, melt 4 tablespoons of the butter. Add the flour and cook over moderate heat, stirring, until smooth, about 1 minute. Whisk in the reserved porcini liquid and the milk. Bring to a simmer and cook over moderately low heat until thickened, about 5 minutes. Stir in the cream and chopped porcini mushrooms. Scrape into a large bowl.

In a large skillet, melt the remaining 2 tablespoons of butter. Add the mushrooms, season with salt and pepper and cook over moderately high heat until browned in spots, about 5 minutes. Add the mushrooms to the porcini sauce. Stir in the pasta and fontina cheese and season with salt and pepper. Scrape the pasta into an 8 1/2-by-12-inch baking dish.

Sprinkle with the Parmigiano-Reggiano and bake for about 35 minutes, until golden and bubbly. Let stand 5 minutes before serving.

The recipe can be prepared through Step 4 and refrigerated overnight. Bring to room temperature before baking. The baked pasta can be refrigerated overnight. Reheat before serving.