Preheat oven to 350 degrees F. Grease and flour a 10 inch bundt pan (see notes)
In the bowl of your mixer, mix the 4 eggs and white and brown sugar at medium-high speed until the mixture thickens and pales in color (approximately 3 minutes).
With the mixer on low speed, add vegetable oil, melted butter, and vanilla extract. Add the sweet potatoes and mix until combined. Do not over-mix.
In a separate bowl, combine the all purpose flour, cinnamon, nutmeg, baking powder, baking soda, and salt. Whisk until well blended.
With the mixer on low speed, alternately add the flour mixture and the milk to the sweet potato mixture, beginning and ending with the flour mixture. After the last addition of flour, mix just until combined- be careful not to over-mix. (We do three additions of flour mixture and two additions of milk.)
Pour the batter into the prepared bundt pan.
Bake at 350 degrees F for approximately 50 minutes. Baking times may vary. Check at 45 minutes as ovens and pan size can effect bake time. The cake is done when a toothpick inserted into the center comes out clean or with just a few crumbs attached.
Let the cake cool in the pan on a wire rack for 5-10 minutes, then turn out.