Preheat the oven to 325. Prep your Bundt pan by spraying it with a cooking spray meant for baking—one with flour in it—or some melted shortening. Make sure the entire inside of the pan is well coated and then lightly dust the entire inside of the pan with granulated sugar.
In the bowl of a stand mixer sift together flour, baking powder, salt, baking soda, and 1 ¼ cups of sugar.
In a small bowl, mix the melted butter, buttermilk, vegetable oil, vanilla, buttermilk and egg yolks until combined.
In a separate, clean bowl of your stand mixer use the whisk attachment to beat the egg whites until foam, about a minute. Lower the speed to medium low and add in the remaining ¼ cup of sugar while the mixer is still running. Allow the egg whites to beat until stiff peaks form, just about a minute. Set aside.
With the bowl containing the flour mixer, use the whisk attachment on low and slowly add the butter mixture to your flour while mixing, about 15-20 seconds. Scrape down the sides of the bowl and the whisk and mix again at medium low until the mixture is combined, about 15 more seconds. Fold in about ½ of the whipped egg whites until combined and then gently fold in the rest, taking care to make sure it’s fully incorporated, and no streaks remain.
Pour your batter into the prepared Bundt pan. Bake for 45-50 minutes, or until a toothpick comes out completely clean.
Allow the cake to cool for 10-15 minutes. While the cake is cooling prepare the butter-rum sauce. Once the cake has cooled slightly, use a toothpick or a wooden skewer to poke holes all over the bottom of the cake (the exposed part while it is still in the pan) and then pour about half of the butter rum sauce over the cake. Allow the cake to sit for 5-10 minutes so the sauce can be fully absorbed, and then carefully turn out the cake onto a serving plate or cake stand. Pour the remaining sauce evenly over the top of the cake.
Butter Rum Sauce
In a medium sauce pan, melt the butter over medium heat. Add in the remaining ingredients and stir until fully combined. Bring to a boil and boil for 4 minutes, stirring occasionally. Remove from the heat and let cool slightly before pouring on the cake.