Heat the oil and butter in a large skillet set over medium-high heat.
When the foaming subsides, add the mushrooms and cook, sprinkling with salt, until the mushrooms are soft and golden.
Add the peas and cream, bring to a simmer and cook until the mixture thickens.
Meanwhile, cook the pasta according to the package directions, or until al dente.
Drain and add to the skillet, tossing with tongs to coat.
Tear in the prosciutto or drape it over the finished pasta.
Serve with Parmesan cheese.