Make the brown sugar vanilla simple syrup by adding the water, brown sugar, and granulated sugar to a medium saucepan and stirring with a wooden spoon. Heat the syrup over medium heat until the sugar has dissolved. Remove the pan from the heat, stir in the vanilla extract, and allow the syrup to cool completely.

Make the pumpkin cold foam by adding the cream, milk, pumpkin puree, vanilla syrup, and pumpkin pie spice to a tall glass or automatic milk frother. Froth the mixture in the glass with a handheld milk frother or in the automatic milk frother until thick and foamy. Alternatively, you can whisk the pumpkin cold foam vigorously in a bowl until thickened or shake vigorously in a tightly sealed mason jar.

Pour the cold brew in a glass over ice, add the vanilla syrup, and stir the coffee with a long spoon. Pour the pumpkin cold foam over the coffee and sprinkle more pumpkin pie spice on top.