In a bowl, combine 1/2 cup heavy whipping cream, 1 tablespoon granulated sugar, and a splash of vanilla extract. Beat until soft-to-medium peaks form. Refrigerate until ready to use.

In a small bowl, mix 1/4 cup unsweetened cocoa powder, 2 tablespoons granulated sugar, and 1/4 teaspoon pumpkin pie spice. Add 1/4 cup heavy whipping cream and stir until a thick paste forms.

In a small pot, combine 2 1/2 cups whole milk and 1/4 cup pumpkin puree. Warm over medium heat, stirring occasionally, until it begins to simmer, but do not let it boil.

Add the cocoa paste to the warm milk and pumpkin mixture. Whisk until the mixture is smooth and creamy, ensuring there are no lumps.

Pour the hot chocolate into two mugs. Top with the chilled whipped cream and lightly dust with extra pumpkin pie spice. Serve immediately.

Store any leftover hot chocolate in a covered container in the refrigerator for up to 3 days. Reheat slowly on the stovetop or microwave.