Preheat the oven to 350°F / 175°C. Generously butter and coat a 9" cake pan with sugar.
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
With a hand mixer or a stand mixer fitted with the paddle attachment, beat together the butter, oil, and sugar for five minutes.
Beat in the eggs one at a time, waiting until the first egg is fully incorporated before adding the next. With the last egg, add in the vanilla.
Alternate folding in the flour mixture and buttermilk. Start by folding in ⅓ of the flour, then ½ of the buttermilk. Continue until you have used up all of the ingredients. Only fold the mixture just until no flour or buttermilk streaks remain to avoid overmixing.
Pour the batter into your prepared pan, and bake for 45-50 min., or until a toothpick inserted in the center of the cake comes out clean or with a few moist crumbs.
Let the cake cool in the pan for 10-15 minutes, then flip it out onto a wire rack to finish cooling.