Preheat the oven to 350F. Prepare the cake pan. You can use an 8x8 or 9x9 pan. Brush the bottom sides of your cake pans with melted butter. Line the bottom and sides of the pan with parchment paper.
In the bowl of a stand mixer, fitted with the paddle attachment, combine the cake flour, granulated sugar, baking powder, baking soda, and salt. On low speed, mix for 1 minute to combine.
7 ounces cake flour, 7 ounces granulated sugar, ½ teaspoon fine sea salt, 1 ½ teaspoons baking powder, ¼ teaspoon baking soda
In a measuring cup, whisk together the buttermilk, eggs, oil and vanilla. Set aside.
2 large eggs, room temperature, 1½ ounces canola oil, 2 teaspoons pure vanilla extract, 6 ounces buttermilk, room temperature
With the mixer on low-medium speed, add in the softened butter pieces, one or two pieces at a time. Mix until the mixture resembles cornmeal. You should be able to gather a bit in your hand, squeeze and you have a solid piece. This means the butter is evenly distributed.
4 ounces unsalted butter, room temperature
With the mixer still on low, pour in ¼ cup of the buttermilk and mix until the flour mixture is just moistened.
Turn the mixer speed to medium (4 or 6) and beat for *2-3 full* minutes. The mixture should be whipped, thick, and lighter in color. This step is crucial to the
Stop the mixer. Scrape the sides and bottom of the bowl to ensure everything is properly mixed.
On low speed, add the remaining buttermilk and egg mixture in two parts, scraping down the bowl after each addition has been mixed in.
Once all the wet ingredients have been incorporated, give the bowl a final scrape and mix with a spatula. Pour the batter into the pan.
Bake the cake for 30-40 minutes. Start checking the cake at 30-35 minutes to test for doneness. The cake is done when a toothpick comes out clean or with a few moist crumbs, and the top of the cake feels springy and set when touched.
Tap the cake pan firmly against the counter to remove excess steam. If your cake domes at all, use a clean kitchen towel to gently push the dome down. Cool the cake for 15 minutes in the pan.
Run a palette or butter knife around the cake in the pan before turning it out to cool completely on a cooling rack.