Heavily grease a 12-15 cup bundt pan. Heat oven to 350°F and arrange a rack in the middle.
Whisk together the 3 cups of flour, the 1 1/2 teaspoons of baking soda, the 1 teaspoon of baking powder, the 1 teaspoon of cinnamon, and the 1/2 teaspoon of kosher salt in a large bowl.
Mash the 3 very ripe bananas in a large bowl then whisk in the 3 large eggs, the 1 1/2 packed cups of brown sugar, the 3/4 cup milk, 3/4 cup vegetable oil, the 1/2 teaspoon cider vinegar, and the 1/2 teaspoon of vanilla extract until eggs are broken up and incorporated. Add flour mixture to the wet mixture and stir until just moistened with a rubber spatula. Stir in the 1 cup of chocolate chips.
Combine the 12 ounces of cream cheese, 1/2 cup granulated sugar, the 1 large egg, and the teaspoon of vanilla extract in a bowl of a stand mixer fitted with the paddle attachment. Start on low speed then increase to medium speed and beat until completely smooth, about 2-3 minutes.
Pour half of the banana cake mixture into prepared pan. Top with the cream cheese mixture and carefully spread into an even layer leaving about an inch border around the outside. Top with remaining banana cake.
Bake until a toothpick inserted in the center comes out clean or with a few moist crumbs, about 60-70 minutes. Let cool in pan on a wire rack for 30 minutes. Run a knife in between the cake and the pan then invert pan to remove cake. Continue cooling on the wire rack.
While the cake is cooling make the glaze. Combine the 4 tablespoons soft butter, 3/4 cup powdered sugar, 3 tablespoons bourbon, and 1/4 teaspoon kosher salt in a medium bowl. Whisk to combine.
Once cake is cooled, spoon glaze over the top. Slice and serve!