Gelato has more air than traditional American ice cream, so the consistency should be creamy, but light.
In a medium saucepan, combine milk and 12 sprigs mint. Bring to a gentle boil, cover, and remove pan from heat. Let steep 30 minutes. Strain mixture; reserve milk, and discard solids.
Combine egg yolks and sugar in the bowl of an electric mixer. Beat at medium-high speed until very thick and pale yellow, 3 to 5 minutes. Return milk to heat and bring to a simmer.
Add half of the milk to egg-yolk mixture; whisk until blended. Return new mixture to saucepan with remaining milk. Cook over low heat, stirring constantly, until mixture is thick enough to coat the back of a wooden spoon.
Remove saucepan from heat; immediately stir in cream. Pass mixture through a sieve set over a medium mixing bowl. Place bowl in ice-water bath, stirring from time to time. Stir in peppermint extract. Freeze in an ice-cream maker according to instructions. Finely chop remaining sprigs of mint. Add mint and chopped chocolate; mix in machine until combined, about 30 seconds. Store in an airtight container.
For the best flavor, soften it slightly in the refrigerator before serving.