Preheat the oven to 350°F. Lightly spray two 9-inch cake pans with baking spray. Line the bottoms of the pans with parchment paper and spray the tops of the paper as well. Set the pans aside. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt; set aside. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and vegetable oil until well mixed. Add both the granulated sugar and brown sugar, then beat on medium speed for about 3 minutes until fluffy. Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract. Add half of the dry ingredients to the wet mixture and mix until just combined, followed by half of the buttermilk, mixing again. Repeat with the remaining dry ingredients and buttermilk, scraping down the sides of the bowl as needed to ensure everything is fully incorporated. Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula for even baking. Bake for 22 to 28 minutes or until a toothpick inserted in the center comes out clean. Allow the cakes to cool completely in the pans. Once cooled, trim any domed or uneven parts from the tops of the cakes if needed, then prepare the frosting. In a medium saucepan, combine the light brown sugar, dark brown sugar, butter, and salt. Place over medium heat and whisk continuously until the butter and sugars melt together. Stir in the evaporated milk and heavy cream, whisking to combine. Bring the mixture to a simmer and cook for 4 minutes until it begins to thicken. Immediately transfer the mixture to a heatproof bowl. Using an electric hand mixer, gradually add the sifted powdered sugar until fully incorporated, then mix in the vanilla extract. Work quickly to frost the cake while the frosting is still spreadable. Place one cake layer, top side up, on your serving plate. Spread ¾ cup of the frosting evenly over the top using an offset spatula or similar tool. Place the second cake layer on top with the flattest side facing upward. Cover the sides and top of the cake with the remaining frosting as quickly as possible before it sets. Let the cake sit for about 2 hours to allow the frosting to harden completely before slicing and serving.