Preheat the oven to 350 degrees F. Lightly spray two 9-inch cake pans with baking spray. Place parchment paper in the bottom of the pans.
In a medium-sized bowl, stir together the flour, baking powder, baking soda, and salt.
Using an electric mixer, mix the butter with the oil until combined. Add the granulated sugar and brown sugar and beat them together on medium speed for 3 minutes.
Add the eggs one at a time until fully mixed in. Stir in the vanilla extract and add half of the dry ingredients and mix until combined but don't overmix.
Next, add half of the buttermilk, and stir until combined. Repeat with the remaining dry ingredients and buttermilk, scraping down the sides as needed.
Divide the batter between the two cake pans. Take a spatula and smooth out the top, this will ensure the cakes bake evenly.
Bake for 22-28 minutes, until a toothpick inserted into the center comes out clean. Don't overbake the cakes. Allow the cakes to cool completely.
While the cakes cool prepare the frosting. Place the light brown sugar, dark brown sugar, butter, and salt into a medium-sized saucepan.
Place the saucepan over medium heat and whisk constantly until the butter and the sugars are melted. Pour in the evaporated milk then the heavy cream, and whisk to combine.
Bring to a simmer and simmer for 4 minutes, it will start to thicken. Immediately pour into a heatproof bowl.
Using an electric hand mixer, add the powdered sugar a little at a time until fully mixed in, and then mix in the vanilla. Mix on high speed for 3-4 minutes. The frosting will be runny but it will set nicely once you frost the cake.
When the frosting is done, we need to work fast to frost the cake while it is still spreadable.
Place one of the cakes top side up onto your serving platter. Add ¾ cup of the frosting and using an off-set spatula or something similar, spread it out over the top of the cake.
Place the other cake top side down on top. Frost the sides and top of the cake as fast as you can before the frosting hardens.
Allow the cake to sit until the frosting completely hardens, about 2 hours before slicing to serve.