Preheat oven to 350 degrees. Set an oven rack to one-below-the-center.
For the caramel: Spray and flour a 12-cup Bundt pan and set aside. In a heavy bottomed saucepan, bring sugar water to a boil. Cover pan and let boil for 2 min. to wash any sugar crystals off the sides of the pan. Uncover and cook without stirring until sugar starts to get some color. Swirl the pan gently to keep the color even. Once the caramel is a deep amber color, remove the pan from the heat and carefully stir in the cream. Stir until smooth. Let cool to just warm.
For the cake: Whisk cocoa powder and vanilla into the coffee. Whisk coffee mixture together with the caramel mixture and set aside. Sift together cake flour, baking powder and baking soda and set aside. Cream butter and cream cheese together until smooth. Add granulated sugar and brown sugar along with salt and Baker's Brew. Cream until very light and fluffy, scraping the bowl as necessary. This will take about 10 min. Very slowly drizzle in beaten eggs a bit at a time until they are all incorporated. Scrape the bowl as necessary. This should take about 5 to 7 min. Alternately add flour and coffee-caramel mixture like this: half the flour, half the liquid, half of the rest of the flour, the rest of the liquid, the rest of the flour. Allow 5 to 10 seconds of mixing on low speed between each addition. Don't worry if one addition isn't completely incorporated before adding the next. Scrape bowl as necessary. Once everything is incorporated, scrape the bowl well, reaching all the way down into the bottom. Fold gently a few times. Beat on high speed for 3 seconds to make sure everything is well mixed. Scrape batter into the prepared pan. Bake for about an hour until well risen and a knife inserted in the center of the cake comes out clean. Let cake cool in the pan for 20 min. Turn cake out onto a rack and let cool to barely warm before glazing, or, to help the cake cool quickly, wrap it tightly in plastic wrap and freeze or refrigerate until just barely warm and apply the glaze.
For the glaze: Place melted butter, sugar, salt and vanilla in a small bowl. Whisk together, adding a splash of milk at a time until you have a thick, smooth and glossy glaze. Have at least ¼ cup milk on hand. Drizzle glaze over the cake and serve.