Preheat oven to 350ºF degrees. Line a large baking sheet with parchment paper or a silicone baking mat. Lightly flour the baking sheet. Set aside.
In a medium size bowl, whisk together butter, oil, egg, and vanilla until combined. Set aside.
In a large bowl, toss together the red velvet cake mix, flour, and salt. Add the wet ingredients to the dry ingredients and gently mix with a large wooden spoon or sturdy rubber spatula until everything is combined.
Check out this Instagram reel to see how I make my biscotti. Turn dough out onto lightly floured baking sheet and, with floured hands, pat dough into a rectangle about ½" thick. My rectangle was 6" wide and 7 and ½" long (using a ruler or a ruled silicone baking mat is helpful here). Brush entire slab (top and sides) with egg wash, if using.
Bake dough slab for 18 minutes, or until the slab looks set. Remove from the oven, but do not turn off the heat. Place baking sheet on a wire rack and allow to cool for 10 minutes. Once the dough is cool enough to touch, cut into 1" thick slices using a sharp knife. Cut these 1" slices in half, making a perpendicular slice down the entire slab. Set slices cut sides up on the baking sheet. Return to the oven to bake for 6 minutes. Remove from oven, turn biscotti over, and bake the other side for 6 minutes. Remove from the oven and allow to cool for 3 minutes on the baking sheet (cookies will become crunchy as they cool). Transfer biscotti to a wire rack to cool completely before serving. Decorate with white, milk, or dark chocolate and sprinkles, if desired. You can also leave them plain or give a simple dusting of powdered sugar. Biscotti stay fresh in an airtight container up to 2 weeks. Baked biscotti may be frozen up to 3 months.