Make the cinnamon-vanilla vodka: Pour the vodka into a jar; add the cinnamon sticks and cover. Store in a cool, dark place, shaking the jar every day or so, for 1 week. Strain; discard the cinnamon sticks.
Make the martini: Coat the rim of a martini glass with marshmallow cream (if it's too thick for rimming the glass, mix with some water). Sprinkle some graham cracker crumbs and cocoa powder on the marshmallow cream. Lightly toast the marshmallow rim with a kitchen torch.
Put 1 ounce of the cinnamon-vanilla vodka, the Drambuie, chocolate liqueur and chocolate bitters in a cocktail shaker filled with ice; shake until frothy. Strain into the prepared martini glass. Rinse out the shaker and refill with ice. Add the heavy cream and honey and shake vigorously (without the ice) until slightly thick. Spoon the heavy cream mixture over the cocktail. Garnish with a toasted marshmallow.
Photograph by Kana Okada
Recipe adapted from The Peninsula for Food Network Magazine