Put some simple syrup in one saucer and some crushed graham crackers in another. Dip the rim of a martini glass into the simple syrup and then into the crushed graham crackers. Set aside.
Add ice to a cocktail shaker. Add the vodka, apple juice, pumpkin spice and 1/2 ounce simple syrup; shake well. Strain into the prepped martini glass. Top off with the pumpkin beer to just below the graham cracker rim.
Combine the sugar with 1/2 cup water in a small saucepan and bring to a light simmer. Cook until the sugar is dissolved, then remove from the heat and let cool completely.