Preheat the oven to 325°F / 162°C. Line a 9x13-inch (quarter sheet) pan with parchment paper. Place two flower nails/heating cores in the center of the pan with the flat side sitting against the cake pan (make sure they are a few inches apart). Spray the pan and flower nails with nonstick baking spray.
Place 1 cup of butter and 1 1/2 cups of 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 as air is incorporated into it.
Mix in 4 eggs on a low speed, two at a time. Scrape down the sides and bottom of the bowl as needed with a rubber spatula.
In a separate bowl, whisk together the 3 cups cake flour, 1 Tbsp baking powder, and 1 tsp salt.
Add half the dry ingredients into the butter/egg mixture and mix on a low speed until combined.
Then mix in 1 cup buttermilk, 1/3 cup oil, and 1 Tbsp vanilla extract on a low speed.
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 with a rubber spatula.
Pour the batter into the prepared pan. Reposition the flower nails so that they’re evenly spaced across 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. Once it's fully cooled, carefully flip the cake and remove the heating cores.