Combine half-and-half and milk in a heavy saucepan; bring to a boil.
Combine 1/2 cup sugar and egg yolks; beat with a mixer at high speed until thick and pale. Gradually add half of hot milk mixture to yolk mixture, stirring constantly with a whisk. Return milk mixture to pan. Reduce heat to medium-low, and cook 2 minutes or until a thermometer registers 160°, stirring constantly. Remove from heat. Place pan in a large ice-filled bowl. Cool milk mixture completely, stirring occasionally.
Combine remaining 1 cup sugar and 1/2 cup water in a microwave-safe dish; microwave at high 2 1/2 minutes or until sugar dissolves. Add mint to hot syrup; steep for 5 minutes. Remove mint; discard. Pour syrup over berries; let stand for 20 minutes. Add berries and syrup to milk mixture; stir well. Cover and chill, stirring occasionally.
Pour mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon the ice cream into a freezer-safe container; cover and freeze for 1 hour or until firm.