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, until the mixture thickens.
Allow pumpkin syrup to cool in the saucepan, then transfer to a clean reusable bottle and seal tightly with a lid. Place in the refrigerator overnight or until it's completely cool.
Add heavy cream, 2% milk, and 1 ounce (30 ml) of pumpkin syrup to a high powdered blender. Blend until a thick foam has formed, about 45 seconds.
To serve, add ice to a serving glass along with cold brew coffee and additional pumpkin syrup or maple syrup to sweeten to taste. Top with pumpkin cold foam mixture, and optionally, sprinkle with additional pumpkin pie spice.