Heat the oven to 350°F (175°C). Thoroughly grease and flour a 10-inch Bundt pan, or coat it with baking spray that contains flour, making sure to cover every ridge and the center tube.

If using nuts, sprinkle the finely chopped pecans or walnuts into the bottom of the prepared pan. Whisk the flour, baking powder, baking soda, and salt together in a separate bowl.

Beat the softened butter and granulated sugar for 3–5 minutes, until pale and fluffy. Add the eggs one at a time, scraping down the bowl after each addition, then mix in the vanilla.

Add the dry ingredients in three additions, alternating with the buttermilk and beginning and ending with the dry mixture. Mix only until combined, then fold in the rum and nuts if using.

Transfer the batter to the Bundt pan and smooth the top. Bake for approximately 50–60 minutes, until a skewer comes out with a few moist crumbs and the cake pulls slightly from the sides of the pan.

While the cake bakes, bring the butter, sugar, and water to a boil in a saucepan. Simmer for 3–5 minutes, stirring until the sugar dissolves, then remove from the heat and carefully stir in the rum and optional vanilla.

Cool the cake in the pan for 10–15 minutes, then pierce it repeatedly with a skewer or toothpick. Slowly spoon or brush about two-thirds of the warm syrup over the cake, pausing so it can absorb.

Let the cake rest in the pan for at least 30 minutes before inverting it onto a serving plate. Brush the remaining syrup over the exposed cake, then cool completely before slicing.