Warm your oven to 350°F before you begin. Lightly coat two 9 inch round cake pans with baking spray, then line the bottoms with parchment paper. Give the parchment a light spray as well, and set the pans aside.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt until everything is evenly combined.

Using a stand mixer fitted with the paddle attachment, or a large bowl with a hand mixer, beat the softened butter and vegetable oil together until smooth. Add the granulated sugar and brown sugar, then continue mixing on medium speed for about 3 minutes, until the mixture looks light and creamy.

Add the eggs one at a time, beating well after each addition so the batter stays smooth. Mix in the vanilla extract until fully incorporated.

Reduce the mixer speed and blend in half of the flour mixture just until combined. Pour in half of the buttermilk and mix gently. Repeat with the remaining dry ingredients and the rest of the buttermilk, scraping down the bowl as needed. Mix only until no dry streaks remain.

Divide the batter evenly between the prepared cake pans. Smooth the tops with a spatula so the layers bake nice and level.

Bake on the center oven rack for 25 minutes. The cakes are ready when a toothpick inserted into the middle comes out clean. Since every oven bakes a little differently, rely on the toothpick test rather than the clock. Leave the cakes in their pans until they have cooled completely.

Once the cakes are cool, trim away any rounded tops if needed to create flat, even layers. Then prepare the frosting.

In a medium saucepan, combine the light brown sugar, dark brown sugar, butter, and salt. Set the pan over medium heat, whisking constantly until the butter has melted and the sugars have dissolved into a smooth mixture.

Whisk in the evaporated milk and heavy cream. Bring the mixture to a gentle simmer and let it cook for about 4 minutes, stirring often, until it begins to thicken slightly. Immediately transfer it to a heatproof mixing bowl.

Using a hand mixer, gradually beat in the sifted powdered sugar a little at a time until the frosting becomes smooth and creamy. Finish by mixing in the vanilla extract.

This frosting firms up quickly, so assemble the cake as soon as it is ready. Place one cake layer on your serving plate with the top facing upward. Spread about ¾ cup of frosting evenly over the surface.

Set the second cake layer on top, placing the flattest side facing up for a neat finish. Quickly spread the remaining frosting over the top and around the sides before it begins to set.

Allow the finished cake to rest for about 2 hours so the frosting can firm up completely. Once set, slice and serve.