Preheat the oven to 350 F. Lightly butter three 9-inch springform pans and line their bases with parchment paper.
Whisk together the flour, baking soda, salt, and cocoa powder, then sift to remove any lumps.
Beat the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment until very light yellow and fluffy, about 5-8 minutes on medium-high speed. Scrape down the sides of the bowl with a flexible spatula, then add the olive oil and mix for 2 minutes on medium speed.
Blend in the eggs and vanilla, then scrape the sides of the bowl and the beater. Mix in the vinegar and food coloring or natural food dye until well combined.
Add half of the dry ingredients and gently fold them in with the spatula. The best way to fold is to scrape around the edges of the bowl in one stroke, then cut through the center of the batter. Repeat until mixed. Fold in all the buttermilk, then fold in the remaining dry ingredients. Be careful not to overmix, but be sure there are no white lumps or streaks in the batter.
Gently divide the batter among the prepared pans. Tap each pan on the counter a few times to get rid of any large air bubbles in the batter.
Bake at 350 F for 15 minutes, switching the pans around after 10 minutes to ensure an even bake. It's done when its surface just barely springs back when gently touched, and when a toothpick inserted into the center comes out clean.
Let them cool for 10 minutes in the pans, then remove from the pans and let cool completely on wire racks, about 45 minutes to 1 hour.