Rub the juicy side of the lemon wedge onto the outside lip of the glass, then roll the glass into one tablespoon cinnamon-sugar and set aside.
In the bottom of a cocktail shaker, muddle the apple and syrup. Add ice and the rest of the ingredients and the remaining cinnamon-sugar. Shake vigorously until the outside of the shaker is frosted and beaded with sweat. Strain into prepared martini glass.