Preheat your oven to 350°F (175°C). Butter and flour a bundt pan or spray it generously with baking spray.
Evenly sprinkle the chopped pecans or walnuts over the bottom of the pan. These will form a delicious, crunchy topping once the cake is flipped out.
Step 2: Make the Buttered Rum Glaze
In a medium saucepan, melt ½ cup butter over medium-high heat.
Add 1 cup sugar, ¼ cup water, and 1 teaspoon pumpkin pie spice. Bring to a gentle boil, then reduce the heat to medium and cook for 3 minutes, whisking occasionally.
Remove from heat and carefully stir in ½ cup dark rum. The mixture will bubble, so pour slowly and stir until smooth. Set aside to cool slightly.
Step 3: Mix the Dry Ingredients
In a medium bowl, sift together flour, pudding mix, baking powder, baking soda, and salt. Set aside.
Step 4: Cream the Butter and Sugar
In a large mixing bowl, use an electric mixer to beat 1 cup butter, 2 cups sugar, and 1 teaspoon vanilla extract on medium-high speed for about 2 minutes or until creamy and light.
Add the eggs one at a time, beating well after each addition. Scrape down the sides of the bowl to ensure everything is evenly combined.
Step 5: Combine the Wet and Dry Ingredients
In a small bowl, whisk together ¾ cup buttermilk (or whole milk) with ¼ cup dark rum.
With the mixer on low, alternate adding the dry ingredients and the milk mixture to the butter-egg mixture, beginning and ending with the dry ingredients. Mix until smooth and fully combined, but do not overmix.
Step 6: Bake the Cake
Pour the batter into the prepared bundt pan over the nuts and smooth the top with a spatula.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean. While the cake bakes, prepare to finish it with the glaze.