Bring a large pot of water to a boil and salt it. When it boils, cook pasta until it is tender but not mushy. Drain pasta, reserving about 1/2 cup of cooking liquid.
Toss pasta in a warmed bowl with 2 or 3 tablespoons cooking liquid, the butter, mint and half the cheese. Taste and adjust seasoning, then serve, passing remaining Parmesan at the table.