Preheat your oven to 350°F (175°C). Grease a 10- to 12-cup Bundt pan thoroughly, paying attention to the center tube and decorative grooves. Lightly dust the pan with flour if necessary, then tap out the excess.
In a medium bowl, whisk together the flour, baking powder, and salt. Mixing these ingredients first helps distribute the raising agent evenly throughout the cake.
In a large mixing bowl, beat the softened butter and granulated sugar for 3–5 minutes, until the mixture becomes pale and fluffy. Proper creaming helps incorporate air into the batter, contributing to a tender cake.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until the batter is smooth. Scrape the sides of the bowl occasionally to ensure the ingredients are evenly incorporated.
Add the dry ingredients in batches, alternating with the milk and rum. Begin and finish with the dry ingredients, mixing on low speed just until combined. Fold in the chopped pecans or walnuts if you are using them. Avoid overmixing, as this can make the cake dense.
Pour the batter evenly into the prepared Bundt pan. Smooth the top with a spatula and gently tap the pan on the counter to release large air bubbles.
Bake for 50–60 minutes, or until a wooden skewer inserted into the thickest part of the cake comes out clean or with a few moist crumbs. If the top browns too quickly, loosely cover it with foil near the end of baking.
While the cake is baking, combine the butter, sugar, and water in a small saucepan. Heat over medium-low heat, stirring until the butter melts and the sugar dissolves. Simmer gently for 2–3 minutes, then remove from the heat. Stir in the rum and vanilla extract carefully. Avoid prolonged boiling after adding the rum if you want to retain more of its aroma.
Let the cake rest in its pan for approximately 10–15 minutes. Use a skewer to make small holes across the exposed surface if needed. Slowly spoon or brush some of the warm syrup over the cake while it is still in the pan, allowing it to absorb gradually.
Carefully invert the cake onto a serving plate or wire rack. Brush the remaining syrup over the golden crust, allowing it to soak in between applications. Let the cake cool completely before slicing so that the syrup distributes evenly.
Serve the cake as it is, or garnish it with chopped pecans, a light dusting of powdered sugar, or thin orange zest strips. Slice into portions and enjoy with coffee, tea, or a scoop of vanilla ice cream.