Combine the milk, chilies, and cinnamon sticks in a heavy large saucepan. Bring to a simmer over high heat. Remove from the heat. Cover and steep for 15 minutes. Whisk in the espresso, sugar, and 1 cup of cocoa powder. Bring the hot chocolate to a simmer, whisking often. Discard the chilies and cinnamon sticks.
Meanwhile, whisk the powdered sugar and remaining 1/4 cup cocoa powder in a large bowl to blend. Add the cream and whisk until the mixture is thick.
Ladle the hot chocolate into 8 mugs. Spoon the chocolate whipped cream atop and serve immediately.