In a light-colored saucepan over medium heat, melt the butter, stirring frequently. It will foam, then the foam will subside — keep going until the butter turns a deep golden amber and smells nutty, about 5–8 minutes. Watch it closely; it can go from browned to burnt quickly. Pour immediately into a large bowl or stand mixer bowl and let cool to room temperature before using. Don’t clean the pan because you will use it again for browned butter frosting.

Preheat your oven to 325°F. Grease three 8-inch round cake pans, line the bottoms with parchment paper, lightly spray the sides and bottom. Set aside.

In a medium bowl, whisk together the cake flour, baking powder, and salt until evenly combined. Set aside.

In a large bowl or stand mixer with the paddle attachment, beat the browned and cooled butter, granulated sugar, brown sugar, and vegetable oil on medium-high for 4–5 minutes, until very light, fluffy, and noticeably paler in color. Scrape down the sides and bottom of the bowl. There's often a hidden pocket of butter at the bottom.

With the mixer on medium, add the eggs one at a time, beating about 30 seconds after each and scraping down the bowl between additions. Add the vanilla with the last egg. If the batter looks slightly curdled, don’t stress, it will come together.

Add the flour mixture in 3 additions, alternating with the buttermilk in 2 additions, starting and ending with flour (flour → buttermilk → flour → buttermilk → flour). Mix on low for each addition and just until combined. Scrape the sides and bottom of the bowl one final time, then fold the batter a few times by hand with a spatula. Don't overmix.

Divide the batter evenly among the three pans (about 19-20 ounces in each pan) — a kitchen scale helps with even layers. Smooth the tops with an offset spatula. Bake for 25–28 minutes, rotating halfway through, until a toothpick comes out with just a few moist crumbs and the edges are just pulling away from the sides. While the cakes are baking, make the caramel and brown butter for the frosting.

Cool in the pans on a wire rack for 10–15 minutes. Run a thin knife around the edges, turn the layers out, and peel off the parchment. Let cool completely before frosting.

In a medium heavy-bottomed saucepan, combine the sugar, water, and corn syrup. Gently stir to moisten all the sugar, then stop stirring.

Set the pan over medium heat and cook undisturbed for 5–10 minutes, until the mixture turns deep amber. Meanwhile, warm the heavy cream in the microwave for about 1 minute.

Once the caramel is a rich copper color, remove from heat and carefully pour in the warm cream.
Caution: The mixture will bubble up rapidly. Pour slowly and whisk constantly.

Whisk until smooth. Stir in the vanilla, salt, and butter. Return to low heat briefly if needed to smooth it out.

Let cool slightly, then transfer to a heat-safe jar and refrigerate until ready to assemble.
The caramel will thicken as it cools.

In a medium saucepan, melt 1½ cups (3 sticks) of unsalted butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter foams and turns a deep deep golden amber and smells nutty.

Immediately transfer the browned butter to a large heatproof bowl and stir in ½ cup (1 stick) of unsalted butter until fully melted and incorporated. This helps rehydrate the browned butter and improve the frosting’s consistency.

Let the butter cool to room temperature (about 2 hours) before using.

When ready to frost, place the room temperature browned butter and cream cheese into the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed for 2–4 minutes until light and fluffy.

Add the powdered sugar, heavy cream, vanilla, and salt. Mix on low to combine, then beat on high for 2 more minutes.

Use a rubber spatula or wooden spoon to beat out any air pockets before frosting.

Place a small dollop of frosting in the center of a cake board to act as glue.

Add the first cake layer top-side up. Spread about 1 cup of frosting over the top and drizzle with caramel sauce.

Add the second cake layer top-side down and repeat the frosting and caramel.

Add the final cake layer top-side down again.

Apply a thin crumb coat of frosting and chill the cake for 15 minutes.

Frost the entire cake with the remaining brown butter frosting. Add a caramel drip if desired and serve extra caramel on the side.
This cake is best served at room temperature for the perfect texture and flavor. I highly recommend it.