Add the pumpkin puree, sweetened condensed milk, water, pumpkin pie spice, vanilla extract, and fine salt to a small saucepan. Whisk over medium heat for about 2 minutes until fully smooth.

Reduce heat to medium-low and simmer for 8 to 10 minutes, stirring every 2 minutes, until the sauce thickens and coats the back of a spoon.

Remove from heat and pour through a fine-mesh strainer into a glass jar, pressing gently with a spatula. Let cool to room temperature for about 20 minutes.

Spoon 2 to 3 tbsp into a mug, add espresso or strong coffee, stir, top with steamed milk, and finish with a dusting of pumpkin pie spice on the foam.