Add brown sugar, maple syrup, pumpkin puree, water, and pumpkin pie spice 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 to a serving glass along with cold brew coffee, and additional pumpkin syrup or maple syrup to taste to sweeten. Top with pumpkin cold foam mixture and optionally sprinkle with pumpkin pie spice.