Preheat the oven to 325°F (165°C). Line the bottom of the pan with parchment paper.
In a large bowl, sift the flour, cocoa powder, 1 cup of the sugar, the five spice powder, cinnamon, baking powder, and salt. Use a large spoon to make a well in the center of the flour mixture.
Add the oil, egg yolks, water, and vanilla to the well and combine the liquid ingredients, then gradually begin to draw in the flour ingredients. Switch to an electric mixer on medium speed and beat the mixture until smooth and thick, about 3 minutes. Stop the mixer and scrape the sides of the bowl as needed.
In a large bowl using clean beaters, beat the egg whites and cream of tartar on low speed until the whites are foamy and the cream of tartar dissolves. Increase the speed to medium and beat the egg whites until they look shiny and smooth and the beaters leave lines in the whites. When you stop the mixer and lift the beaters, the beaten whites should cling to them. Increase the speed to high and slowly beat in the remaining 1/2 cup sugar, 1 tablespoon at a time. Beat until the whites form firm, glossy peaks, about 1 minute.
Use a rubber spatula to fold the chopped milk chocolate into the reserved cocoa and egg yolk mixture. Stir about 1/3 of the beaten whites into the yolk mixture, then gently fold in the remaining whites until no white streaks remain. Scrape the batter into the prepared pan and gently smooth the top.
Bake until the top of the cake feels firm when lightly touched and any small cracks on the top look dry, about 1 hour and 10 minutes. Invert the pan onto a narrow-necked bottle (a full wine bottle works well) and let cool for 1 hour.
Turn the pan right side up and run a thin, sharp knife around the side of the pan and the center tube to loosen the cake. Turn the cake onto a wire rack so it is bottom up, remove parchment paper. Cool the cake thoroughly on the wire rack.