Whisk whole milk, vanilla, sugar, cocoa, 1 teaspoon of cinnamon and chili powder in a heavy saucepan.
Add 2 of the cinnamon sticks and cook gently over medium-low heat until warm.
Add chocolate and cook, whisking until the chocolate is completely melted. Gently simmer until liquid thickens and reduces slightly, whisking often, about 10 minutes.
Combine heavy cream with remaining 1/2 teaspoon cinnamon and beat until peaks form. Ladle 1/3 cup hot cocoa into 6 mugs; top with whipped cream and garnish with a cinnamon stick.