Combine the mint and milk in a blender (or food processor) until the mint is finely chopped.

Transfer the mint mixture to a heavy-bottomed medium-sized pot. Add the cream and sugar and stir to dissolve.

Place the pot on the stove over medium heat and heat the mixture until it just begins to bubble. Remove the pot from the heat, cover it, and let the mixture steep for one hour.

Once the mixture finishes steeping, place a sieve over a large bowl and strain the mint from the infused cream, milk and sugar. Press down on the mint leaves in the sieve to ensure you extract all the liquid and discard the mint.

Place the bowl in an ice water bath, in the freezer or refrigerator, until cold.

Once cold, freeze it in an ice cream maker, according to the manufacturer's instructions.

Combine the chocolate and oil and melt the chocolate in a double boiler over just simmering water, or in the microwave (if using a microwave, check on the melting process periodically, stirring each time you check, so the chocolate does not burn). Once melted, set aside.

Five minutes before the ice cream is finished churning, drizzle the melted chocolate into the ice cream while the machine is still running.