Bring 3-4 quarts salted water to a rapid boil.
When water is boiling, cook pasta for 10-12 minutes, or according to package instructions. (Before draining pasta, reserve ½ cup of the cooking water.)
While the pasta is boiling, wash the carrot greens thoroughly then chop.
Heat the olive oil in a large sauté pan over medium-high heat.
Add the garlic and sauté until it starts to turn golden brown, about 1 minute.
Turn the heat to medium-low and add the basil, mint, lemon zest, carrot greens and corn. Saute until the greens have just wilted, about 2-3 minutes. (Do not overcook.) Remove from heat.
When pasta is cooked, drain, remembering to reserve ½ cup of the liquid.
Add the cooked pasta to the sauté pan with the cooking water and toss thoroughly.
Toss with the cheese before serving.