To make this dessert, inspired by a hot-chocolate drink, flavored with cinnamon, you'll need an ice-cream maker.
Prepare an ice bath (fill a bowl with ice and water). Combine cocoa, dark-brown sugar, granulated sugar, expresso powder, cinnamon, anise, salt, and 5 cups of water in a large saucepan over medium-high heat. Bring to a boil; reduce to a simmer, stirring occasionally, for about 15 minutes. Remove from heat, and pour through a fine sieve into a bowl set in the ice bath. Chill.
Freeze in an ice-cram maker according to manufacturer's instructions. Freeze overnight. Serve garnished with bunuelo sticks.