On a small plate, stir together 1 teaspoon corn syrup and the brown sugar. Dip the rims of 4 martini glasses in the mixture, then in the chopped nuts.
In a cocktail shaker filled with ice, combine 1/4 cup vodka, 1/4 cup corn syrup and 1/2 teaspoon vanilla. Strain into 2 prepared glasses. Repeat with the remaining ingredients.