Gather all ingredients and ensure everything is at room temperature. Preheat your oven to 325°F (165°C). Grease and flour a Bundt pan thoroughly or use a non-stick baking spray.
In a mixing bowl, combine flour, sugar, pudding mix, salt, nutmeg, and baking powder. Add softened butter and vegetable oil. Mix until the texture resembles damp sand. Beat in eggs, one at a time. Alternate adding milk and rum, mixing until just combined. Stir in vanilla extract.
Grease the Bundt pan thoroughly. Sprinkle chopped pecans at the bottom of the pan for added texture and flavor.
Pour the batter into the prepared Bundt pan. Bake at 325°F (165°C) for 55–60 minutes, or until a skewer inserted comes out clean. If using a dark pan, reduce baking time slightly.
In a saucepan, melt butter over medium heat. Stir in sugar and water. Bring to a boil, then reduce heat and simmer for 5–8 minutes without stirring. Remove from heat and carefully stir in the rum and vanilla extract.
While the cake is still warm and in the pan, poke holes all over the surface using a skewer. Slowly pour half the warm rum syrup over the cake. Let it soak for 10–15 minutes before inverting onto a wire rack. Brush or drizzle the remaining syrup over the top and sides of the cake.
Let the cake rest for a few hours before slicing for best flavor. Serve at room temperature or slightly warmed. Store wrapped at room temperature for up to 5 days or refrigerate for longer shelf life.