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For the pumpkin spice syrup, add the water, brown sugar, spices, and pumpkin puree in a small saucepan.
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Whisk to combine, and heat over medium high heat until simmering.
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Reduce heat to low, and simmer for about four minutes, until thickened.
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Whisk in the vanilla, remove from heat, and cool.
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Transfer to a storage container. It should keep about a week in the refrigerator.
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For the pumpkin spice latte, brew some espresso or strong coffee.
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While that is brewing, heat up the milk in the microwave (or on the stovetop, if you prefer).
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Optional: use a stick blender to froth up the milk. Just blend on medium-high for about 30 seconds.
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Add a tablespoon of the syrup to the milk.
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Pour in your coffee, and stir to combine.
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Optional: sprinkle with cinnamon. If you are feeling more indulgent, top with caramel sauce and/or whipped cream.