Preheat oven to 350°F (175°C). Grease the sides of three 8-inch cake pans, line the bottoms with parchment circles sized to fit, and grease the parchment.
In a medium bowl whisk together 2 1/4 cups all-purpose flour, 2 teaspoons baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt. Set aside.
In a smaller bowl whisk together 2 tablespoons cocoa powder, 1 tablespoon vinegar, 2 teaspoons vanilla extract, and 1 tablespoon red gel food coloring until smooth and evenly colored.
In the bowl of a stand mixer (or a large bowl with a hand mixer) cream 1/2 cup softened butter and 1 1/2 cups sugar on medium speed until light and fluffy, about 2–3 minutes. Scrape down the bowl as needed.
Add the cocoa-color mixture to the creamed butter and sugar and beat until incorporated. Add the 2 eggs, one at a time, beating until each is fully incorporated and the batter is smooth.
With the mixer on low, add half of the dry flour mixture and mix until just incorporated. Add half of the 1 cup buttermilk and mix until smooth. Repeat with the remaining flour mixture and the remaining buttermilk, mixing until the batter is smooth and uniform.
Divide the batter evenly among the three prepared pans and smooth the tops. Bake 30–35 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pans for 5 minutes, then run a knife around the edges, invert the cakes, and transfer to a wire rack to cool completely.
Using a serrated knife, level and remove the domes from each cooled cake. Break the trimmed pieces into crumbs and spread them in an even layer on a baking sheet.
Bake the crumbs on the baking sheet for 15 minutes to dry them. Let the crumbs cool completely.
Place the cooled crumbs in a food processor and pulse until very fine (about 30 seconds–1 minute). Set the fine crumbs aside.
For the frosting base (stabilized roux): from the 3/4 cup unsalted butter measured for the frosting, measure out and melt 2 tablespoons in a small saucepan over medium heat. Whisk in 2 1/2 tablespoons all-purpose flour and cook, whisking constantly, for 1 minute.
Gradually whisk in 1/2 cup milk, 1/2 teaspoon vanilla extract, and 1/4 teaspoon salt. Whisk constantly until the mixture thickens into a paste (about 1 minute). Transfer the paste to a small bowl, press plastic wrap directly onto the surface to prevent a skin, and cool completely (refrigerate to speed cooling if desired).
Transfer the cooled paste to a larger mixing bowl. Add the remaining butter from the 3/4 cup (the rest of the measured 3/4 cup), 8 ounces softened cream cheese, and beat until smooth and well combined. Add 1 cup icing sugar and beat until the frosting is smooth and creamy. If the frosting is too soft, chill briefly and rebeat.
To assemble the cake, place four 6x6-inch parchment squares overlapped on your cake platter to protect the platter. Set one cake layer in the center (right-side-up) and spread about 3/4 cup of frosting evenly over the top.
Place the second cake layer on top and spread another 3/4 cup of frosting evenly over that layer.
Place the final cake layer on top with its top-side-up. Use the remaining frosting to cover the top and sides of the cake evenly.
Sprinkle about 1/2 cup of the fine cake crumbs over the top and gently press them into the frosting. Press additional crumbs onto the sides with your hands or a spatula until the cake is evenly coated.
Carefully pull out the parchment squares from under the cake, wipe any stray crumbs from the platter, slice, and serve.