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In a large skillet, melt butter over medium heat. Add onion, season lightly with salt, and cook until softened but not brown, about 6 minutes. Stir in prosciutto cotto, rosemary, thyme, and 1/4 teaspoon pepper. Cook until prosciutto cotto is warmed through and herbs are fragrant, about 4 minutes.
Add wine and cook until reduced by half, about 2 minutes. Add cream and nutmeg, bring to a simmer, and cook, stirring occasionally, until sauce is slightly thickened, about 2 minutes. Reduce heat to low to keep sauce warm, or turn off heat while pasta cooks if your stove isn't capable of cooking below a simmer.
Meanwhile, in a pot of salted water, cook pasta until just shy of al dente (about 2 minutes less than the package directs). Using a spider skimmer, transfer pasta to sauce, along with 1/2 cup (120ml) pasta cooking water. Alternatively, drain pasta using a colander or fine-mesh strainer, making sure to reserve at least 1 cup (240ml) pasta cooking water.
Increase heat to high and cook, stirring and tossing rapidly, until pasta is al dente and sauce is thickened so that it coats noodles and just pools around edges of the pan, about 2 minutes; add more pasta cooking water in 1/4-cup (60ml) increments as needed to achieve desired consistency.
Remove from heat, add peas and grated cheese, and stir rapidly to incorporate and heat peas through. Season with salt and pepper to taste. Serve immediately.