Prepare a 9-inch spring form pan: Cut a circle of parchment the size of the removable bottom of the pan. Fit the parchment circle into the bottom of the pan. Tear off an 18-inch length of aluminum foil. Center the pan over the sheet of foil and crumple and crimp the foil all around the sides of the pan. (The foil will prevent water from seeping into the pan during baking.) Set the pan aside.
In a medium saucepan, bring the espresso, brown sugar and the cinnamon sticks to a simmer over very low heat. Simmer until the syrup is very fragrant, about 20 minutes. Stir in the butter until melted, and then stir in the cayenne pepper. Set aside.
Pulse the chocolate in the food processor until coarsely chopped. Transfer to a deep bowl. Pour in the warm coffee syrup and whisk until the chocolate is completely melted. Whisk in the beaten eggs until completely blended.
Scrape the batter into the prepared pan. Set the pan in a large, deep, oven-proof skillet or a roasting pan and set on the oven rack. Pour in enough water to come halfway up the sides of the pan. Bake until center is set and barely wiggles when you shake the pan gently, 50 to 60 minutes.
Cool the cake to room temperature. Remove the foil and chill the cake in the pan at least 8 hours. Run a wet knife around the sides of the pan then pop the spring to release. Place a platter on top of the cake and flip over. Remove the bottom of the pan, and peel off the parchment. Serve with cinnamon ice cream and raspberries.