In a heavy bottomed saucepan, heat 1 cup cream, whole milk, 1/2 cup sugar, and mint and basil leaves over medium-low heat, stirring often. When mixture just begins to steam, remove from heat, cover, and set aside to steep for 1 hour.

Strain herb infusion with a mesh strainer, pressing leaves to release all possible liquid. Discard leaves. Reheat herb-infused cream over medium-low heat, just until small bubbles form along the sides and mixture begins to steam.

Place yolks in a medium bowl and whisk with 2 tablespoons sugar. To temper the yolks, whisking constantly, add 1/4 cup of the warm cream; still whisking, add another 1/4 cup, and then another. Add one cup total, then stir yolk mixture into the warm cream. Cook, stirring constantly, over medium-low heat for 5 minutes. Remove from heat. (If desired, strain mixture before chilling.) Stir in the remaining cup of cream.

Set mixture over and ice bath to chill quickly or cover and refrigerate overnight.

Process ice cream according to your ice cream maker's instructions.

Meanwhile, melt chocolate over a double boiler, stir in the remaining 2 tablespoons sugar plus a generous pinch of sea salt.

Drizzle melted chocolate over the bottom of a freezer-proof container. Add a layer of ice cream, followed by a layer of chocolate. Continue alternating layers. Cover container and freeze until cured, 4 - 5 hours or longer.

Serve with a sprig of fresh mint.