Using tongs, transfer pasta to pot with mushrooms and add 1 cup pasta cooking liquid.
Crumble half of prosciutto into pot.
Increase heat to medium, bring to a simmer, and cook, tossing constantly, until pasta is al dente and liquid is slightly thickened, about 2 minutes.
Add cream, return to a simmer, and cook, tossing, until pasta is coated, about 1 minute.
Remove from heat, add butter, and toss to combine.
Taste and season with salt if needed.