In a medium saucepan, combine half of the milk (1 cup) with the white chocolate and cocoa powder. Cook over medium heat, stirring periodically, until the chocolate is melted and the mixture is well combined.
Stir in the pumpkin puree and pumpkin pie spice. Continue to cook while occasionally stirring until heated through.
Add the remaining milk and cook until heated through.
If using freshly roasted pumpkin instead of canned pumpkin, I recommend pouring the hot chocolate through a fine mesh sieve to eliminate any chunks. Canned pumpkin is much smoother.
Serve topped with freshly whipped cream and a dash of nutmeg.