Preheat your oven to 325°F (163°C). Generously grease and flour three 8-inch round cake pans or spray them with non-stick baking spray to ensure easy release.
In a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the butter and vegetable oil together on high speed for 2 minutes until smooth and creamy. Gradually add the granulated sugar and continue beating on high speed for 4–5 minutes, until the mixture becomes very pale yellow, light, and fluffy.
Add the eggs one at a time, mixing well after each addition. Scrape down the sides and bottom of the bowl as needed to ensure everything is fully incorporated. Mix in the vanilla extract.
In a separate bowl, sift together the cake flour, baking powder, salt, and baking soda. With the mixer on the lowest speed, slowly add the dry ingredients to the wet ingredients in two additions. Be careful not to overmix—just mix until the flour is incorporated.
Finally, add the sour cream and heavy whipping cream, mixing just until the batter is smooth and fully combined. Scrape down the bowl one last time and give the batter a gentle final mix by hand if needed.
Divide the batter evenly between the prepared cake pans. Bake for 17 to 24 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Do not overbake. Begin checking for doneness around 16 minutes, as oven temperatures can vary.
Remove the cakes from the oven and let them rest in the pans for 10–15 minutes. Carefully invert them onto wire racks and allow them to cool completely before assembling.