Heat 2 Tbsp. oil in a Dutch oven or other large pot over medium-high. Cook half of mushrooms in a single layer, undisturbed, until edges are brown and starting to crisp, about 3 minutes. Give mushrooms a toss and continue to cook, tossing occasionally, until all sides are brown and crisp, about 5 minutes more. Using a slotted spoon, transfer mushrooms to a plate; season with salt. Repeat with remaining 2 Tbsp. oil and mushrooms and more salt.

Reduce heat to medium-low and return all of the mushrooms to the pot. Add shallots and cook, stirring often, until shallots are translucent and softened, about 2 minutes.

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente, about 2 minutes less than package directions.

Using tongs, transfer pasta to pot with mushrooms and add cream and 1 cup pasta cooking liquid. Increase heat to medium, bring to a simmer, and cook, tossing constantly, until pasta is al dente and liquid is slightly thickened, about 3 minutes.

Remove pot from heat. Add lemon zest and juice, parsley, butter, ½ oz. Parmesan, and lots of pepper and toss to combine. Taste and season with more salt if needed.

Divide pasta among bowls and top with more Parmesan.