In a blender combine avocado, half-and-half, powdered sugar, finely shredded lemon peel, and lemon juice. Cover and blend until smooth. Pour avocado mixture into a 2-quart square baking dish. Cover and freeze for at least 4 hours or until firm.
To serve, let stand at room temperature for 15 minutes. Cut into squares and divide among serving bowls. If desired, garnish with lemon peel strips and/or mint leaves.