Place a small saucepan over medium-low heat. Pour in the milk and whisk in the pumpkin puree until the mixture is smooth and the pumpkin is fully incorporated into the liquid. This ensures a consistent texture without pumpkin clumps.

Add the white chocolate chips and the pumpkin pie spice to the saucepan. Continue to whisk constantly. Make sure the heat stays low enough that the milk does not come to a boil, as boiling can cause the white chocolate to seize or the milk to scorch on the bottom of the pan.

Once the chocolate has completely melted and the drink is steaming hot, remove the pan from the heat. Stir in the vanilla extract. Adding the vanilla at the end preserves its aromatic flavor. If you want a frothier texture, use a hand frother for about 30 seconds until a light foam forms on top.

Pour the hot chocolate into two large mugs. Top generously with whipped cream and a sprinkle of pumpkin pie spice or a drizzle of caramel sauce for that authentic coffeehouse look. Serve immediately while hot.