In a medium saucepan set over medium heat, whisk together the half-and-half (or milk), pumpkin puree, vanilla syrup, pumpkin pie spice, and salt until smooth and steaming (do not bring to a boil). Remove from the heat and stir in the vanilla extract.
Strain through a fine mesh sieve into a jar; allow to cool. Put a lid on the jar and refrigerate until chilled (at least 1 to 2 hours).
Pour 1 cup of cold brew coffee into a glass and stir in desired amount of vanilla syrup. Fill glass with ice to the top of the coffee level.
Pour ¼-cup of Pumpkin Cream into a 1-cup glass measuring cup or a frothing pitcher. Use a milk-frother to froth the milk to desired consistency. Pour over the top of the iced coffee, sprinkle with pumpkin pie spice (if desired), and serve immediately.
