Make the syrup. Add the water and sugar to a small pot. Heat over medium heat. Split the vanilla bean lengthwise and scrape out the seeds inside and add them to the pot. Throw in the bean pod as well. Cook until the mixture becomes thick like a syrup. Let it cool.
Make the sugar for the rim of the glasses. Split the vanilla bean lengthwise and scrape out the seeds inside and add them to the sugar. Mix the sugar and vanilla well so the vanilla gets distributed evenly in the sugar. Dip the rim of the glasses in water and dip them in the vanilla sugar to coat well.
To make the martini, add all the ingredients to a martini shaker and pour into the sugar rimmed glasses.