1. Prepare an ice-water bath. Cook mint in a small saucepan of boiling water until bright green, about 1 minute. Using a slotted spoon, transfer mint to ice-water bath. When cool, drain, and squeeze out excess water. Reserve ice-water bath.

2. Puree mint and milk in a blender until mint is finely chopped. Transfer to a medium saucepan, add cream, and bring to a simmer over medium heat.

3. Meanwhile, whisk together eggs and sugar in a medium bowl.

4. Gradually whisk 1/3 of the cream mixture into the egg mixture, then pour egg-cream mixture into the saucepan with the remaining cream mixture. Set over medium heat, and cook, stirring constantly with a wooden spoon, until thick enough to coat the back of the spoon, about 8 minutes. (Do not let the mixture come to a simmer.)

5. Strain through a fine sieve into a heatproof bowl, pressing on mint to extract liquid. Set bowl in ice-water bath. Let cool completely, stirring occasionally. Freeze in an ice cream maker according to manufacturer's instructions. Transfer to an airtight container, and freeze until firm, about 4 hours (or up to 1 week).