In a large mixing bowl, whisk together the half-and-half and granulated sugar until fully dissolved, about 2-3 minutes.

Stir in the heavy cream, vanilla extract, mint extract, sea salt, and green food coloring. Mix well for 1-2 minutes.

Pour the mixture into your ice cream maker and churn according to the manufacturer's instructions, typically around 20 minutes.

During the last 5-10 minutes of churning, add the finely chopped semisweet chocolate and milk chocolate.

Check if the mixture reaches a soft-serve consistency and stop the machine when it's thick enough.

Transfer the ice cream mixture into an airtight container and press plastic wrap onto the surface to minimize ice crystals.

Place the container in the freezer for at least 4-6 hours until fully set.