Place a large pot of salted water over high heat and bring to a boil. Once boiling, add the pasta and cook according to package directions. Drain and reserve the pasta in the cooking pot.
While the pasta is cooking, combine garlic, cream, limoncello and lemon peel over medium-high heat in a medium-size saucepot. Bring the mixture to a gentle boil, then reduce the heat and simmer until slightly thickened, about 10 minutes. Remove the garlic clove and lemon peel from the sauce and discard.
To the pot with the reserved pasta, add the sauce, the basil and a couple handfuls of Parmigiano Reggiano. Season with salt and freshly ground black pepper, and toss to combine.
To serve, top each portion with additional Parmigiano-Reggiano and some lemon zest.