Pour the milk into a saucepan and warm it over medium heat, stirring gently until it begins to steam and small bubbles form around the edges.
Add the pumpkin puree, sugar, cinnamon, nutmeg, cloves, and ginger to the warm milk. Whisk constantly to combine and break up any lumps until the mixture is smooth and heated through, about 3-5 minutes.
Reduce the heat to low and add the vanilla extract. Continue whisking until the mixture is velvety and just beginning to simmer, ensuring all the flavors meld together.
Remove the saucepan from heat and stir in the liquor, adding it gradually and tasting as you go to achieve your preferred boozy level.
Pour the hot chocolate into mugs, then optionally top with whipped cream and a sprinkle of pumpkin spice for an extra cozy touch.
Savor immediately while warm, enjoying the rich aroma and smooth, spiced flavor with each sip.