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.
To make the glaze:
In a small saucepan, dissolve brown sugar into cream over medium-low heat. When combined, add rum and set heat to low. Allow to simmer until liquid is reduced and thickens. Add butter and stir to melt, then remove from heat.
Using a skewer, poke multiple holes across the bottom of the cake. Spoon or brush buttered rum glaze on the cake, and allow to soak 5-10 minutes, then repeat with more glaze two more times. Let cake soak & cool 20-30 minutes.
When cake is cooled, turn it out onto a cake plate. Brush top and sides of cake with remaining glaze, making multiple passes over it until it's all used up.
Top with whipped cream or ice cream if desired before serving. Enjoy!