Preheat oven to 325°F (163°C). Spray two 9-inch round cake pans with baking spray, line with parchment paper, and spray again.
In a large bowl, whisk together the red velvet cake mix and instant chocolate pudding mix until well combined.
In another bowl or stand mixer, combine eggs, milk, sour cream, oil, vanilla extract, white vinegar, and food coloring (if using). Mix on low speed for 30 seconds.
Add dry mixture to wet ingredients. Mix on low for 30 seconds, scrape bowl, then beat on medium for 2 minutes until smooth.
Divide batter evenly between prepared pans. Bake for 28-32 minutes until a toothpick inserted in center comes out with moist crumbs.
Cool cakes in pans for 15 minutes on wire racks, then invert onto racks, remove parchment, and cool completely (about 1 hour).
Beat cream cheese and butter on medium speed for 3-4 minutes until fluffy. Add vanilla and salt, then gradually add powdered sugar. Beat on medium-high for 2-3 minutes.
Level cake layers with a cake leveler or serrated knife to remove any domed tops.
Place first layer on serving plate, spread 1½ cups frosting on top. Add second layer, apply thin crumb coat, refrigerate 30 minutes, then frost with remaining frosting.