Pour chocolate syrup onto a shallow plate. Dip the rims of martini glasses into the chocolate syrup to coat them. Drizzle the inside of each glass with chocolate syrup.

In a large cocktail shaker, combine Baileys, chocolate liqueur, and vodka. Fill the shaker with ice and shake vigorously until thoroughly chilled, about 20 seconds.

Divide the mixture evenly between the prepared glasses. If desired, top each martini with shaved chocolate for an extra touch of indulgence.

Serve and enjoy the luxurious blend of chocolate and spirits in every sip!