Whisk the half-and-half and sugar in a large bowl until the sugar is completely dissolved.

Add the heavy cream, mint extract, vanilla extract, sea salt, and a few drops of green food coloring, if using. Stir until fully combined.

Pour the mixture into your ice cream maker and churn according to the manufacturer's directions.

After about 20 minutes of churning, add the chopped semisweet and milk chocolates.

Continue to churn for another 5–10 minutes, checking for a soft-serve consistency. Avoid over-churning.

Transfer the ice cream into an airtight freezer-safe container. Press plastic wrap directly onto the surface of the ice cream to reduce ice crystal formation.

Freeze for several hours or until firm enough to scoop.