Preheat oven to 350°F (177°C).
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, cream the butter and granulated sugar together until light and fluffy (about 4-5 minutes). Beat in eggs one at a time, then beat in the egg yolk and pure vanilla extract, stopping to scrape down the sides of the bowl as needed.
In a separate mixing bowl whisk together the cake flour, baking powder, and salt. Set aside.
In a large measuring cup whisk together the buttermilk and rum. Set aside.
Alternate mixing the dry ingredients with the buttermilk rum mixture into the wet ingredients in three additions, starting and ending with the dry ingredients.
Generously spray a 10-inch (12-cup) bundt pan with nonstick cooking spray, making sure to fully coat the entire pan. Sprinkle the chopped nuts into the pan and spread them around in an even layer. Scoop the batter into the prepared bundt pan over the chopped nuts and spread it around into one even layer.
Bake at 350°F (177°C) for 40-55 minutes or until a toothpick inserted into the cake comes out clean. Cover loosely with foil for the last 5-10 minutes of baking time if needed to prevent excess browning.
Remove the cake from the oven and place it on a wire rack to cool slightly in the pan while you prepare the glaze.