Preheat the oven to 350F (180C).
Add the chopped pecans to a cookie sheet in a single layer. Bake in the preheated oven for 8-10 minutes, or until golden and you can smell the aroma. Do not let the nuts burn. Remove from the oven and turn the oven down to 325F (160C).
Grease a bundt pan generously and dust with flour. Be sure to coat every crevice, especially around the center. Alternatively, brush with pan release (AKA cake goop).
Whisk together the cake flour, baking powder and salt. Set aside.
In a large bowl, whip the 3 egg whites using the whisk attachment of your mixer. Once frothy (about 2 minutes) add in ¼ cup sugar and continue whipping until stiff peaks form (about 1 more minute). Set aside.
In a large bowl, beat together the butter and the remaining 1 ½ cups sugar until fluffy. Mix in the oil and vanilla extract. Then mix in the 5 egg yolks.
Sift in about ⅓ of the flour mixture. With the mixer on a low speed or using a wire whisk, carefully mix in the flour mixture.
Whisk in the the milk. Stop mixing as soon as it's combined.
Sift in about ⅓ more of the flour. Then carefully whisk it into the batter. Whisk in the rum.
Sift in the last of the flour and whisk until the batter is smooth. Stop mixing as soon as everything is combined. Overmixing will lead to a dry cake.
Using a rubber spatula, gently fold the egg whites into the batter. Continue to fold them into the batter until you no longer see streaks of egg white.
Sprinkle the toasted, chopped pecans into the bottom of the prepared bundt pan (if you're using pecans). Then pour the cake batter over top.
Bake in the preheated oven for about 60-75 minutes, or until an inserted toothpick comes out clean and you see the edges starting to pull away from the pan. The bake time will vary depending on the size of your bundt pan and your oven.
Transfer the pan to a wire rack and cool for at least 15 minutes. Then carefully invert the pan to release the cake. If it appears to be stuck, gently tap on the sides of the pan to help release the cake.