Sift the cake flour, cocoa powder, baking soda, and salt into a medium bowl and set aside.
Add the softened butter to a large bowl or the bowl of a stand mixer. Beat with an electric mixer or with the paddle attachment in the stand mixer until smooth and creamy. Gradually add the granulated sugar and mix on low speed until combined. Once all of it is added, turn the speed up and beat until well combined, light, and fluffy.
Add the room temperature eggs, one at a time, and mix on low speed until just combined after each. Wipe the sides of the bowl with a rubber spatula, then add the vanilla extract, white vinegar, and buttermilk, and mix until smooth. The batter will look lumpy once you add the buttermilk, but it will fix itself once the dry ingredients are added.
Add the sifted dry ingredients and mix on low speed or whisk by hand until the batter is smooth. Use a whisk to mix in enough red gel coloring until you're happy with the color.
Pour the batter into the bundt pan, use a spatula to spread it out evenly, and bake in the preheated oven for 35-40 minutes. A toothpick inserted into the center should come out mostly clean or with a few crumbs.
Once the pan is cool enough to hold, place an upside down plate, cooling rack, or a cake board over the top and flip the pan over to invert the cake onto it. The cake will come out easier while it's still slightly warm.
Let the cake cool at room temperature, then refrigerate until cooled completely before frosting.