To make the cake, preheat the oven to 350 degrees F (180 C). Thoroughly coat the inside of two 8-inch round cake pans with softened butter, then dust lightly with flour, tapping to shake out the excess. Set cake pans aside.
In a large bowl, combine the 3/4 cup butter, granulated sugar, and salt, mixing by hand until creamed together. Whisk in the oil, followed by the eggs, buttermilk, vanilla, and food coloring, whisking until mixture is smooth.
Sprinkle the flour, cocoa powder, and baking soda on top of the wet ingredients, then whisk gently just until combined.
Divide batter evenly between the two pans, and bake for 22-25 minutes, until a toothpick inserted into the center comes out clean or with moist crumbs, and the sides just start to pull away from the edges of the pan. Allow cakes to cool in the pans for 10-15 minutes, then invert onto wire racks to cool completely before frosting.
To make the frosting, combine the cream cheese and butter in a large bowl or the bowl of a stand mixer. Using either a hand mixer or the stand mixer fitted with the paddle attachment, beat on medium-high speed for 2-3 minutes, until the mixture is light and fluffy. Add powdered sugar and mix on low speed just until incorporated, then add the vanilla, increase the speed to medium-high, and beat 2-3 minutes more. Frost cake as desired.