In a small saucepan over medium heat, combine the brown sugar, 1 teaspoon pumpkin pie spice, and 1/2 cup water. Stir until the sugar is dissolved and bring it to a boil. Remove from heat and cool for 30 minutes. Syrup can be stored in the refrigerator for up to 2 weeks.
Mix together the granulated sugar and remaining 1 teaspoon pumpkin pie spice and put it onto a shallow plate. Pour 2 tablespoons of the simple syrup onto a plate. Dip the rims of 4 martini glasses into the syrup, and then in the spiced sugar. Set aside.
In a large measuring cup, combine the half-and-half, pumpkin puree, vanilla, and half the simple syrup and whisk until well blended. Pour in to a pitcher filled with ice. If using the vodka, add it to the pitcher before serving and stir. Pour into the prepared glasses. Top with sparkling water.