Combine the brown sugar, water, ground spices, and vanilla extract in a small saucepan. Gently bring the mixture to a boil, stirring occasionally, until the brown sugar dissolves. Reduce heat and simmer for an additional 2-3 minutes, allowing the syrup the syrup to cool before pouring it into a jar for storage in the fridge for up to 2 weeks.
Meanwhile, add the milk to a small saucepan and heat over low heat until warmed to your liking.
In a microwave-safe bowl, heat the white chocolate chips in the microwave for 30-second increments until they have melted. It will likely only take 30 seconds to fully melt the chips, and you may need to stir them to get them to melt entirely. If you overheat the chips, they tend to harden and don't mix as well into the drink.
Stir the pumpkin puree and espresso into the melted chips before pouring into your favorite mug. Add 1-2 tablespoons of your pumpkin spice syrup.
If you want to add body to the drink, froth the milk just before adding it to your mug. Stir to combine, and enjoy! For extra indulgence, add a dollop of whipped cream and a sprinkling of cinnamon.