In a medium saucepan over medium heat, melt the butter.

Add the pumpkin puree, heavy cream, granulated sugar, brown sugar, pumpkin pie spice, cinnamon, and salt. Whisk until smooth and combined.

Bring the mixture to a gentle simmer, then reduce the heat to low.

Cook for 8-10 minutes, stirring frequently, until the sauce thickens slightly and becomes glossy.

Remove the saucepan from the heat and stir in the vanilla extract.

Let the sauce cool for a few minutes before serving warm, or transfer to a jar and refrigerate for later use.