In a medium saucepan, combine milk, cocoa powder and sugar in pan. Stir to combine and bring to a simmer over low-medium heat, you don't want to boil the milk, just heat gently so that all ingredients are combined.
Using a fork or potato masher (preferred) gently press the chestnuts down, smashing them open and add to saucepan. Stirring to incorporate.
Cook over low heat for 15 minutes, stirring occasionally. Be sure not to let the milk boil.
After 15 minutes, remove the pan from heat and blend on medium with immersion blender until smooth.
Pass the Chestnut Hot Chocolate thru the fine mesh sieve and into 2 glasses. Top with your favorite hot cocoa toppings, I used homemade vanilla bean marshmallows.