Heat the oven to 350°F. Grease a 10 to 12-cup Bundt pan thoroughly, then dust the interior with a little cocoa powder, tapping out the excess.
Bloom the cocoa: In a heatproof bowl, whisk the hot brewed coffee into the sifted dark cocoa powder until silky and no lumps remain. Set aside to cool until warm, about 5 minutes.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
In a large bowl, vigorously whisk the sugar, eggs, and vanilla until slightly thickened and pale, 1½ to 2 minutes. Slowly stream in the oil while whisking until the mixture looks glossy and cohesive.
Whisk in the sour cream and milk until smooth, then whisk in the warm cocoa–coffee mixture until evenly combined.
Switch to a spatula and fold the dry ingredients into the batter in two additions just until no dry streaks remain. Let the batter rest 5 minutes to hydrate the cocoa and settle bubbles.
Scrape the batter into the prepared pan and tap the pan firmly on the counter 2–3 times to release air pockets.
Bake until the top springs back and a toothpick inserted near the center comes out with a few moist crumbs, 40 to 46 minutes. Rotate the pan once if your oven has hot spots.
Cool on a rack for 12 minutes, then loosen the edges with a thin knife and invert onto the rack. Cool completely before glazing.
Make the drizzle: Microwave the cream cheese in a bowl for 10–15 seconds until just pliable. Whisk in the powdered sugar, cocoa, and vanilla. Thin with milk or cream, 1 teaspoon at a time, to a thick-but-pourable consistency. Whisk in the light corn syrup if using for extra sheen.
Spoon or pour the glaze over the cooled cake in slow zigzags, letting it cascade down the sides. Allow 15 minutes for the glaze to set before slicing.