Place first 4 ingredients in a zip-top plastic bag. Seal bag, and crush spices into small pieces using a rolling pin or meat mallet.
Combine crushed spices, milk, brown sugar, and ginger in a medium saucepan. Cook over medium heat 8 minutes, stirring until sugar dissolves and tiny bubbles form at edge of saucepan (do not boil). Remove from heat; cover and let stand 15 minutes.
Add cocoa to milk mixture, and stir. Cook mixture over medium heat 2 minutes, stirring constantly until blended. Strain mixture through a sieve, and serve immediately. Garnish with cinnamon sticks, if desired.