Preheat oven to 350 degrees F. Spray two 9-inch round cake pans with nonstick spray, then line with parchment paper.
In the bowl of your stand mixer, add butter, oil, sugar, vanilla, baking powder, and salt. Mix to combine for about 3 minutes on medium speed.
½ cup unsalted butter, ⅓ cup vegetable oil, 1 ½ cups granulated sugar, 1 tablespoon vanilla extract, 2 ½ teaspoons baking powder, ½ teaspoon kosher salt
Add the eggs and egg yolks, one at a time, scraping down the sides of the bowl between each addition.
4 large eggs, 2 large egg yolks
Mix in half of the flour. Pour in the milk and mix again. Then, mix in the remaining flour until just combined.
3 cups cake flour, 1 cup whole milk
Divide the batter evenly between the two pans.
Bake for 25-35 minutes, or until a toothpick inserted in the center of the cakes comes out clean with just a few crumbs.
Cool completely in the pans, then use a knife to loosen the edges before inverting and removing the cakes.
To make the frosting, add 1 ½ cups butter and brown sugar to a medium saucepan over medium heat.
2 cups unsalted butter, 1 ½ cups light brown sugar
Whisk to combine and cook for 5-8 minutes, stirring intermittently, until the brown sugar has dissolved and turns a light brown color.
Remove from heat and carefully whisk in the ½ cup heavy cream, vanilla, and salt.
½ cup heavy cream + 2 tablespoons, 1 tablespoon vanilla extract, ½ teaspoon kosher salt
Once combined, pour caramel into the bowl of your stand mixer and let cool about 10 minutes.
Using the whisk attachment, beat in the remaining ½ cup butter, powdered sugar and 2 tablespoons heavy cream. Adjust the frosting’s consistency by adding more powdered sugar or heavy cream, but you’ll want the frosting to be thick yet spreadable.
6 cups powdered sugar
To assemble the cakes: Place one layer of cake on a plate or serving dish.
Spread frosting in a thick layer over top. Place the next layer of cake on top. Frost the entire outside of the cake until smooth.
Notes
Butter: If you would prefer to use salted butter, omit the salt in the cake and in the frosting.
Oil: Or another neutral oil like canola oil or light olive oil.
Kosher salt: Sea salt is the best substitute for kosher salt. If you want to use table salt, use 1/4 teaspoon.
Cake flour: Cake flour helps to give this cake its tender crumb. If you don't have cake flour, you can make a homemade cake flour substitute.
Whole milk: The fat in the whole milk helps to add moisture and richness to the cake. You can use a lower fat milk, but you'll lose a bit of the moisture and richness.