Chill a coupe or martini glass in the freezer for 5–10 minutes. Rub the lemon wedge around the rim of the chilled glass, then dip the rim lightly into the confectioners' sugar so a thin sugared rim forms. Set the glass aside.

Build the Cocktail

Fill a cocktail shaker halfway with ice. Add 1.5 oz Smirnoff Vanilla Vodka, 0.5 oz Licor 43, 0.5 oz white crème de cacao, 0.5 oz vanilla cream syrup, and 1 oz half-and-half to the shaker.

Shake

Seal the shaker and shake vigorously for 12–15 seconds until the outside of the shaker is frosty and the mixture is well chilled and slightly frothy from the dairy.

Strain and Garnish

Double-strain the cocktail into the chilled, sugared-rim glass. Carefully grate or shave about 1 tablespoon of white chocolate over the top of the drink. If using the vanilla bean, split 1/4 of the bean lengthwise and scrape a small amount of seeds across the surface for aroma and visual appeal. Serve immediately.