Preheat the oven to 350°F (180°C). Grease and line four small round layer-cake pans.
In a medium bowl, whisk together the flour, cocoa powder, salt, and baking soda.
In a large bowl, whisk the vegetable oil, sugar, vanilla, sour cream, eggs, egg yolk, vinegar, and enough red gel coloring to reach the desired shade.
Gradually add the dry ingredients and whisk until smooth, scraping the sides of the bowl as needed. Do not overmix.
Divide the batter evenly among the prepared pans. Bake for about 15 minutes, until the layers spring back lightly and a tester comes out clean.
Cool briefly in the pans, then turn the layers onto wire racks and cool completely. Level the tops if needed and reserve the trimmed cake for crumbs.
For the frosting, beat the cream cheese, butter, vanilla, powdered sugar, and a pinch of salt until smooth. Avoid overbeating.
Stack the cooled layers with frosting between each one, then frost the top and sides. Decorate with reserved red velvet crumbs and chocolate sprinkles if desired.