Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until just under al dente, 10 to 11 minutes. Meanwhile, once you?ve added the pasta to the boiling water, heat a large straight-sided skillet over medium heat. Add the butter to the hot pan. When the butter is melted, add the garlic and cook, stirring often, until soft and fragrant, about 1 minute. Add 1/2 cup of water from the pasta pot and reduce the heat to low.
When the pasta is ready, transfer it to the pan with the sauce using tongs; reserve the pot of cooking water. Raise the heat to medium and sprinkle 1 1/2 cups of the parmigiano-reggiano onto the plain pasta. Stir with 2 wooden spoons to combine. Add the mascarpone, lemon zest and 3/4 teaspoon salt. Toss well to coat, adding additional hot pasta water as needed to thin the sauce and to finish cooking the pasta. Add the peas, lemon juice and the remaining 1 cup of parmigiano-reggiano. Toss well to combine, adding pasta water as needed to thin the sauce to your desired consistency; you will probably use close to 1 1/2 cups pasta water total. Sprinkle with the ground pink peppercorns and additional parmigiano-reggiano, if desired.