Preheat the oven to 350°F. Line a 9 X 12-inch baking pan with parchment paper and set aside.
In a large bowl, whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer, beat the butter and sugar together on medium speed until creamed together and fluffy. Next, add the oil and mix further until pale and aerated, another minute or two. Stop the mixer and scrape down the sides of the bowl.
With the mixer on medium-low, begin adding in the eggs, one at a time. Allow the eggs to absorb into the batter before adding the next. Add the vanilla extract and mix. Stop the mixer and scrape down the sides of the bowl.
Add about half of the flour mixture and slowly mix until mostly combined. Add the milk, and turn the mixer to medium-low to combine. Add the remaining flour mixture and mix until incorporated. Stop the mixer. Give the batter a few stirs with a rubber spatula to finish mixing until smooth.
Pour the batter into the prepared pan. Bake for 25 to 28 minutes, or until a toothpick inserted into the center comes out clean. Cool the cake on a wire rack before removing from the pan.