Preheat the oven to 325°F / 162°C. Line a 9x13-inch (quarter sheet) pan with parchment paper. Spray the pan with nonstick baking spray.
Place butter and sugar in the bowl of a stand mixer or a large bowl. Beat on a medium-high speed using a whisk attachment for 2 minutes. The mixture should become lighter in color.
2 sticks unsalted butter, 1½ cups granulated sugar
Mix in the eggs on a low speed, two at a time. Scrape down the sides and bottom of the bowl as needed.
4 large eggs
In a separate bowl, whisk together the cake flour, baking powder, and salt.
3 cups cake flour, 1 tbsp baking powder, 1 tsp salt
Add half the dry ingredients into the butter/egg mixture and mix on a low speed until combined.
Then mix in buttermilk, coconut oil, and vanilla extract on a low speed.
1 cup buttermilk, ⅓ cup coconut oil, 1 tbsp vanilla extract
Add in the rest of the dry ingredients and mix until the ingredients are just incorporated. Scrape down the sides and bottom of the bowl as needed.
Pour the batter into the pan. Bang the pan on your counter to remove any air bubbles, then bake for 35-40 minutes. Rotate the pan halfway through to help the cake bake evenly.
Let the cake cool in the pan for about 15 minutes, then carefully remove it from the pan and place it on a wire rack to finish cooling.