Step 1

Heat ¼ cup oil in a large Dutch oven or other heavy pot over medium. Arrange prosciutto in a single layer in pot and cook, turning once or twice, until crisp, about 5 minutes. Transfer to paper towels to drain.

Step 2

Heat remaining 2 Tbsp. oil in same pot over high. Cook mushrooms, tossing occasionally, until browned and tender, 5–8 minutes. Reduce heat to medium-low. Add shallots and 1 tsp. thyme, season with salt and pepper, and cook, stirring often, until shallots are translucent and softened, about 2 minutes. Add stock and reduce heat to low. Bring to a simmer and cook until only a thin layer of stock coats bottom of pot, 5−7 minutes.

Step 3

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente, about 3 minutes less than package directions.

Step 4

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.

Step 5

Divide pasta among bowls. Top with more thyme and crumble remaining prosciutto over; season with pepper.