In a medium saucepan combine cream, sugar, and mint leaves. Cook and stir over medium heat until mixture just begins to boil. Remove from heat; cover; steep for 1 hour. Strain, discarding mint leaves. Add milk to infused cream mixture. Cover and refrigerate for 2 hours or overnight until mixture is completely chilled.
Freeze cream mixture in a 1-quart ice cream freezer according to the directions of the manufacturer. Ripen ice cream according to manufacturers directions. Scoop into dessert dishes. Sprinkle with fresh mint or basil leaves. Makes 1 quart.