Mix 3 tablespoons Oreo cookie crumbs (available in most groceries in baking isle) plus 1 tablesoon powdered sugar on a flat plate. Coat rim of chilled cocktail Martini glass with lime and then dip rim of glass in Oreo mixture. Set aside.
Mix Godiva liqueur, creme de cacao, vodka, and half-and-half into a cocktail shaker filled with ice cubes. Shake vigorously and strain into the set aside cocktail glass. Serve.