Preheat the oven to 325°F. Grease 3 (9-inch) round pans with vegetable shortening and line the bottoms with parchment paper.
Combine the flour, sugar, cocoa powder, baking soda, and salt in the bowl of a heavy duty stand mixer fitted with the whisk attachment.
Slowly add the vegetable oil and butter to the flour mixture until combined. Add the eggs, one at a time, beating just until the yellow disappears after each addition.
Beat in the vanilla, vinegar, and food coloring. Divide the batter evenly between the prepared pans. Bake for 18 to 22 minutes or until a toothpick inserted in the centers comes out clean.
Let cool in the pans for 5 minutes. Run a knife around the edges and turn out onto cooling racks to cool completely.
Make the frosting.
Spread the cream cheese frosting between the layers and on the tops and side of the cooled cakes. Refrigerate until ready to serve.