1 lb. spaghetti
1½ cups shelled fresh peas
½ cup (1 stick) unsalted butter
6 oz. prosciutto, thinly sliced (ABOUT 12 slices)
16 sage leaves
2 oz. Parmesan, finely grated ( about 1 cup ), plus more for serving
Cook pasta in a large pot of boiling salted water, stirring occasionally and adding peas about 2 minutes before pasta is done, until al dente. Drain pasta and peas, reserving 1½ cups pasta cooking liquid.
Meanwhile, heat butter in a large Dutch oven or other heavy pot over medium until frothy. Tear prosciutto slices into bite-size pieces and add to pot along with sage. Cook, stirring occasionally, until prosciutto is golden brown and beginning to crisp, about 4 minutes. Remove from heat and let sit until pasta is done.
Add pasta, peas, 2 oz. Parmesan, and 1 cup reserved pasta cooking liquid to pot with prosciutto and return to medium heat. Cook, tossing vigorously and adding more pasta cooking liquid if needed, until saucy and pasta is coated, about 30 seconds. Taste and season with more salt if needed. Divide pasta among bowls and top with more Parmesan.