Preheat the oven to 350º F and grease a bundt pan, making sure to get inside all the groves, and then dust it with flour. Shake out any excess. You can also use a 9-inch diameter spring form pan.
In a medium bowl whisk the flour, baking powder, and salt together until fully combined.
Using an electric mixer fitted with the paddle attachment cream the butter and sugar until light and fluffy, about 5 minutes.
Add the eggs one at a time scraping down the sides of the bowl after each addition.
In a small bowl whisk the oil, evaporated milk, vanilla extract, and rum together until mixed well.
Add half of the flour mixture and half of the wet ingredient mixture to the bowl of the electric mixer and mix until combined. Repeat with the remaining flour mixture and wet ingredients.
Sprinkle the pecans in the bottom of the prepared bundt pan and pour or spoon the batter on top.
Bake for 1 hour and 10 minutes (check your cake around 50 to 55 minutes and adjust the time accordingly) or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan sitting on a rack.
Prepare the rum syrup by placing the butter, brown sugar, evaporated milk, rum, and vanilla extract into a saucepan set over medium-high heat. Stir until the sugar dissolves and then bring the mixture to a boil, without stirring it. Let it boil for 5 minutes to allow the syrup to thicken and cook down.
Poke holes into the bottom of the cake while it's still in the pan. Drizzle the syrup on top.
Allow it to sit in the pan for 1 hour before removing it to allow the syrup to soak into the cake.