In a large saute pan, heat the butter, white wine, mushrooms and peas. Saute until softened and cooked through, about 8 to 10 minutes.
Bring 6 quarts of water to a boil and add 2 tbsps salt.
Just before the pasta is done, pour a ladle of the starchy cooking water into the pan with the pea puree and stir to loosen the sauce.
Cook the pasta until al dente and drain well, reserving more of the pasta water.
Immediately toss the pasta into the pan with the peas and mushrooms and 1 cup freshly grated Parmesan cheese over medium heat.
Stir gently to mix well, adding a little pasta water to achieve the correct texture, not too dry and not too wet - the noodles should be dressed like the greens of a salad.
For a bit of heat, you can add a pinch of red chili flakes.
Serve immediately.