Coat the rim of the martini glass by dipping it in a shallow dish of chocolate syrup, followed by a plate of cocoa powder or chocolate shavings.
Combine your vodka, chocolate liqueur, and Baileys into a cocktail shaker. Fill with ice cubes and give it a good shake for approximately 30 seconds to ensure the mixture is well chilled.
Carefully pour the strained mixture into the prepared martini glass.
Add a dusting of chocolate shavings, cocoa powder, or a drizzle of chocolate syrup on top before serving immediately.