1. Combine milk, half-and-half, and mint sprigs in a medium heavy saucepan over medium-high heat. Heat milk mixture to 180° or until tiny bubbles form around edge (do not boil). Remove from heat; cover and let stand for 10 minutes.
2. Pour milk mixture through a fine sieve over a bowl, pressing slightly with a wooden spoon; discard solids. Return liquid to pan.
3. Place sugar, salt, and egg yolks in a bowl; stir with a whisk until pale. Gradually add half of hot milk mixture to egg mixture, stirring constantly with a whisk. Pour egg yolk mixture into pan with remaining milk mixture; cook over medium-low heat until a thermometer registers 160° (about 2 minutes), stirring constantly. Place pan in a large ice-filled bowl until custard cools completely, stirring occasionally. Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Drain ice water from freezer bucket; repack with salt and ice. Cover with kitchen towels, and let stand 1 hour or until firm. Garnish with mint leaves, if desired.