Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
Prepare the dry ingredients: In a large bowl, sift together the flour, sugar, baking soda, cocoa powder, and salt.
Mix the wet ingredients: In another bowl, whisk together the oil, buttermilk, eggs, red food coloring, vanilla, and vinegar.
Combine wet and dry ingredients: Slowly mix the wet ingredients into the dry ingredients until just combined.
Bake the cakes: Divide the batter evenly between the prepared pans and bake for 25–30 minutes. Let cool completely.
Make the brown butter pecan frosting: In a saucepan, brown the butter. Let it cool. Beat the cream cheese until smooth, then add the brown butter and vanilla. Gradually add powdered sugar and fold in toasted pecans.
Assemble the cake: Level the cake layers, frost between layers, and decorate with extra pecans.