Preheat oven to 325 degrees F. Spray a 15-cup bundt pan with baking spray, then dust with 3 Tablespoons cocoa powder; set aside.
Whisk flour, baking soda, baking powder and salt together in a medium bowl; set aside.
In a large saucepan set over medium heat, combine butter, buttermilk, hot chocolate, rum, cocoa powder, and spices. Heat until butter melts and all ingredients come together, then whisk in sugars, stirring until dissolved. Cool mixture for 5 minutes, then transfer to a large mixing bowl.
In a small bowl, whisk together eggs and vanilla extract, and add to cooled chocolate rum mixture, stirring until combined.
Add flour mixture and stir until just combined - batter will be rather thin but slightly lumpy/bubbly.
Pour batter into prepared bundt pan. Bake for 50-60 minutes, or until a skewer inserted to the bottom comes out clean. Remove from oven and allow to cool for 20-30 minutes while you prepare the glaze.