Add a few tablespoons chocolate liqueur to a small rimmed plate. Add a few tablespoons cocoa powder to another small plate and whisk briefly to break up the lumps. Dip the rim of a martini glass into the liqueur then into the cocoa. Set aside.
Add the chocolate liqueur, vodka, and half-and-half to a cocktail shaker filled with ice and shake for a good 20 seconds. Pour into rimmed martini glass.