Add brown sugar, maple syrup, pumpkin puree, pumpkin pie spice, and water to a small saucepan and whisk together.
Cook over medium heat until the mixture reaches a boil, about 3 - 4 minutes. Once boiling, cook for an additional 60 seconds, stirring frequently, to allow the mixture to thicken.
Allow pumpkin syrup to cool in the saucepan, then transfer to a cleaned reusable bottle and seal tightly with a lid. Place in the refrigerator overnight to completely cool.
Add heavy cream, 2% milk, and 1 ounce of pumpkin syrup to a high powdered blender. Blend for 45 seconds until a thick foam has formed.
To serve, add ice, 1 cup cold brew coffee, and ½ ounce maple syrup to a serving glass. Top with pumpkin cold foam mixture.