If you're going to make homemade vanilla pudding mix, mix together those ingredients before you begin. Preheat oven to 325 degrees F.
Grease and flour a bundt pan, and sprinkle half of the crushed pecans along the bottom. Some fine pecan dust alongside the larger chunks is just fine. Set aside the pan and the rest of your pecans.
In an electric mixer, cream 1 1/2 cups granulated sugar with 1 stick of butter. Add 3 tablespoons of your olive oil. In a separate bowl, whisk together 1 3/4 cups flour, cornstarch, baking powder, and salt.
With the mixer on low, add the dry mixture to the butter/sugar mixture. Then add in the pudding mix. Scrape down the sides and then turn on the mixer again to combine evenly. The mixture is very dry and will look like fine crumbs.
In a separate bowl, whisk together the eggs, milk, rum, vanilla extract, and remaining 1/2 cup of olive oil. With the mixer on low, add it to the dry mixture and mix well until combined. Pour into your prepared bundt pan.
Mix the rest of your pecans with the extra tablespoon each of flour and sugar. Sprinkle the mixture evenly over the top of the batter.
Bake the cake for 50 to 60 minutes, or until a toothpick inserted in the cake comes up clean. Try a few different areas and if the toothpick comes up clean but glistens slightly, give it an extra 10-15 min. The addition of the pudding mix makes it so that the cake sets, but is still a bit gelatinous. In other words, your cake may need a bit more time in the oven.
Let the cake cool in the pan for 20-30 minutes, then invert onto your serving platter.