Heat together cream, milk, and mint in a medium pot over medium heat until mixture starts to simmer. Remove from heat, cover, and let steep about 2 hours.
Preheat oven to 300°. Set 8 ramekins (4 oz. each) in a large roasting pan or baking dish.
Reheat cream mixture to a simmer; strain into a medium bowl. Whisk together sugar and yolks in a large bowl. Slowly add cream to yolk mixture, whisking constantly.
Pour mixture into ramekins, dividing evenly. Fill pan with hot water until it reaches halfway up sides of ramekins.
Cover pan with foil and bake until custards are set and jiggle only slightly in the center, about 30 minutes. Remove from oven and let sit in hot water 30 minutes. Transfer ramekins to a baking sheet, cover, and chill at least 2 hours and up to 3 days.
Serve with whipped cream, fresh mint leaves, and chocolate shavings.