Toast the marshmallows: Preheat your oven to broil. Place the marshmallows on a parchment-lined baking sheet and broil for about 5 minutes, or until golden brown and toasted. Keep a close eye on them as they can brown quickly.
In a small saucepan, combine the water, brown sugar, granulated sugar, pumpkin puree, and pumpkin spice. Stir well to combine.
Place the saucepan over medium heat and let the mixture cook for about 10 minutes, stirring occasionally, until the sugars have dissolved and the syrup is well combined.
Remove the saucepan from the heat. Add the toasted marshmallows and stir continuously until they have completely dissolved into the syrup.
Allow the syrup to cool before straining into a clean, airtight jar or bottle. Store in the refrigerator and give it a good shake or stir before using.