Chill a martini glass in the freezer for at least 10 minutes.

Rim the chilled martini glass with melted chocolate: Dip the rim of the glass into melted chocolate, rotating it to coat the edge evenly. Allow any excess chocolate to drip off.

Place the chocolate-rimmed glass back into the freezer to set while preparing the cocktail.

Fill a cocktail shaker with ice cubes.

Add vodka, coffee liqueur, chocolate syrup, and cold-brewed coffee to the shaker.

Shake the mixture vigorously for about 15-20 seconds to chill and combine the ingredients well.

Remove the martini glass from the freezer and strain the cocktail into the glass.

Garnish with chocolate eggs.