Bring the water and sugar to a boil, stir to thoroughly dissolve the sugar.
Remove from the heat and let cool.
Transfer the sugar water to a container with a tight fitting lid.
Add vodka, Strega extract, vanilla bean and yellow food coloring.
Mix all together, cover with lid and let it stand in a cool, dark place for about 90 days.
Yellow food coloring gives the Galliano its characteristic look. You can omit this if you like.