Preheat oven to 325 degrees F. Grease and flour a standard Bundt pan (12-cup capacity). Sprinkle the chopped walnuts around the bottom; set aside.
In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt; set aside.
Using an electric mixer on medium speed, cream together the butter and granulated sugar until light and fluffy, about 3 minutes. Add the flour mixture and the 3 tablespoons of canola oil, and mix on medium-low speed for a minute or two - the mixture should look like wet sand. Add the pudding mix and mix again on medium-low speed until combined.
In a medium bowl, whisk together the eggs, milk, rum, remaining ½ cup canola oil, and vanilla extract. Add the egg mixture to the dry ingredients and beat on medium speed until thoroughly combined, about 2 to 3 minutes, scraping the sides of the bowl as needed. (The batter will be quite thin - this is good! It will be nice and moist!)
Pour the cake batter into the prepared Bundt pan and bake for 50 to 60 minutes, or until a tester inserted into the center of the cake comes out clean.
When the cake has about 10 minutes left to bake, start the rum syrup. Melt the butter in a medium-sized saucepan over medium heat. Once it is melted, add the sugar and the water. Boil for 5 minutes, stirring constantly. Turn off the heat and stir in the rum. Once it is mixed in, return it to medium heat for about 30 seconds.
When the cake comes out of the oven, immediately pour about one-third of the rum syrup over the bottom of the cake. Pour slowly so it has time to seep into the cake. Let it sit for 5 minutes.
Invert the cake onto a serving platter. Using a fork or a skewer, poke holes all over the cake - the top, sides, and around the inside. Don't be shy - all of the holes ensure that the rum syrup seeps into the cake evenly. Sloooooowly pour the remaining rum syrup over the top of the cake, allowing it to drip down the sides. You want to do this step very slowly (it took me almost 15 minutes) so that the syrup actually seeps into the cake and doesn't just pool on the bottom of the serving dish.
Allow the cake to cool to room temperature before serving.