To a jar, add the half & half, pumpkin puree, maple syrup and pumpkin pie spice. Stir to combine. Add lid and chill until ready to use.
To prepare drink, either pour mixture into a cocktail shaker or add to a medium bowl to use with an immersion blender. Shake or blend 1 to 2 minutes, until foamy.
To a glass, add the ice and cold brew. Stir in maple syrup, if desired. Top coffee with pumpkin cream foam and garnish with pumpkin pie spice, if desired.