In a saucepan, add the pumpkin puree and half of the granulated sugar. Heat over medium heat, stirring until it reduces to half the amount (approximately 1/2 cup). You can measure this to be sure.
To avoid any sediments, strain your mixture using a fine mesh strainer, assisting with a spoon if necessary.
Add the hot pumpkin mixture, instant coffee, remaining sugar, and boiling water to a mixing bowl.
Whip the mixture with an electric mixer until it becomes fluffy and at least doubles in volume, resembling beaten egg whites in appearance.
Mix in the vanilla extract and pumpkin spice. If anything gets stuck to the sides, pause, scrape with a spatula, and continue mixing for 5-10 minutes.
Pour your pumpkin spice latte mixture into a freezer-safe container, taking care not to overfill. Remember that frozen liquids expand, which may cause your container to crack (as it has happened to me before)
You can now enjoy your pumpkin spice latte. First warm up the milk of your choice (it needs to be really hot) . Then add about a tablespoon of the mixture and whisk it around to dissolve
Freeze any remaining mixture in a freezer-safe container. You'll observe that it won't freeze completely but will firm up while remaining scoopable. That's exactly how it's intended to be. Enjoy!