Add the pumpkin puree to a medium saucepan. Then, add the half and half, brown sugar, maple syrup, cinnamon, and pumpkin pie spice. Whisk until well incorporated. Place over medium heat for 10 minutes, just until the liquid begins to bubble around the edges of the pan.Remove from the heat. Cool at room temperature for 10 minutes.Transfer to a sealed container. Store in the refrigerator for up to 7 days.Shake or stir well before adding desired amount to coffee.