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Set a large pot of salted water to boil for the pasta.
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Heat a large nonstick skillet over medium heat. Add 2 tablespoons of butter and 1 tablespoon of olive oil. When it is melted, add the sliced mushrooms with a sprinkle of salt. Cook until all of the liquid has cooked out of the mushrooms and evaporated, about 10-15 minutes. Toss occasionally and add a little more salt and pepper to taste. Transfer the mushrooms to a bowl and set aside.
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Heat the remaining oil and butter in the same skillet. When it is hot, add the red onion. Cook for 2 minutes, and then add the asparagus. Toss to coat with butter and oil. Cook, stirring occasionally, for 7 minutes.
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Add the cream and asiago fresco cheese with the mushrooms and garlic. Sprinkle in some salt and pepper. Reduce the heat to low and stir the cream and cheese in. Let it simmer for 10 minutes.
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In the meantime, cook the pasta until al dente. Drain into a colander but be sure to reserve 1 cup of the cooking water.
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Transfer the cooked pasta back into the pot. Dump the sauce on top of the fettuccine and add the sauce on top of the pasta. Add the Parmigiano cheese and the Prosciutto ham. Toss. Add pasta cooking water as necessary to loosen the sauce up. Taste for salt and pepper. Serve, sprinkled with additional Parmigiano cheese.