In a very large pot, bring 5 quarts water and 3 tablespoons salt to a boil. Add the pasta and cook until just al dente, about 1 minute less than the package directions. Occasionally give the pasta a stir so it doesn’t stick together. Scoop out and reserve 1 cup of the pasta water before draining the pasta.
Meanwhile, put a large skillet over medium heat. Add the pancetta and cook until almost crisp, about 3 minutes. Don’t drain off the fat. Add the garlic to the pan and stir, making sure it doesn’t brown, for 30 seconds.
Add the reserved pasta water and the peas. Simmer for 1 minute.
Add the cooked pasta to the pan, stirring the noodles into the sauce, and cook for 30 seconds. Remove from the heat and stir in the mint, Parmesan, and olive oil. Taste and adjust the seasoning, adding additional Parmesan if desired. Serve immediately.