Step 1

For the rim: In a small bowl as wide as the glass, whisk together the powdered sugar and half-and-half. (The icing should be very thick.) Place the sprinkles on a small plate. Dip just the rims of two coupe glasses into the icing, twisting to coat. Immediately dip the frosted rims into the sprinkles. Refrigerate until ready to use.

Step 2

For the martini: In a cocktail shaker, combine the vanilla vodka, Irish cream liqueur, butterscotch schnapps, half-and-half, and ice. Cover and shake vigorously for 10 to 20 seconds. Strain into the chilled coupe glasses and serve immediately.