Mix the cream and mint together in a small saucepan and bring to a simmer. Remove from heat and let steep for 15 min. Remove the leaves by draining with a strainer. Let the cream cool and then refrigerate until cold.
Rub the rim of the martini glass with sliced piece of fruit, like a grape or strawberry to get it slightly damp. Then rim the glass with the finely grated chocolate.
In a cocktail shaker filled with ice add the vodka, Baileys, and the cooled cream. Shake and pour into prepared martini glasses. Garnish with more grated chocolate and mint leaves.