Preheat the oven to 350°F. Butter and flour a bundt pan or liberally spray with baking spray. Sprinkle pecans evenly on bottom. Set aside.
Using an electric mix, cream together butter, sugar and vanilla on medium-high for 2 minutes, or until creamy. Add eggs one at a time beating well after each addition.
In a separate bowl, sift together flour, pudding mix, baking powder, baking soda and salt. A whisk works perfectly.
Whisk together buttermilk and rum.
With the mixer on low speed gradually add dry ingredients alternately with wet ingredients beginning and ending with flour. After all is added, beat just until fully combined stopping to scrape the sides of the bowl occasionally.
Bake for 50-60 minutes or until a cake tester inserted into the center of the cake comes back clean.
About 10 minutes before the cake is finished baking, make the buttered rum glaze.
To make the glaze: In a medium saucepan, melt the butter over medium-high heat. Add the sugar, water and pumpkin pie spice. Bring to a boil, then lower to medium cooking for 3 minutes, whisking occasionally. Remove from heat and add rum. Be careful the mixture may foam up. Continue to stir until foam dies down, placing back onto the stovetop with the heat turned off. Cook for 1 minute then set aside.
When cake is finished baking, remove from the oven. Use a long thin skewer to poke holes over the bottom of the cake. Slowly pour 1/2 buttered rum glaze over bottom of cake allowing it to soak in between pours. Let cake sit for 1 hour to cool in the pan.
Carefully turn cake onto a platter or stand. Use the same skewer to poke holes in the top of the cake. Try to poke between the pecans. Slowly pour remaining glaze into holes on top of cake. Be patient this will take several minutes. The slower you go, the more glaze goes into the cake and doesn't pool on platter. (It may be necessary to warm the glaze slightly before pouring onto the top.)
Once cooled, cover and chill for at least 1 day. The rum flavor mellows the longer this cake proofs.
You may also make this cake using buttered rum flavoring in place of alcohol. When doing so, use 1-2 tsp in the cake. For the glaze, use 1-2 tsp in place of rum.