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To make the cake:
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Heat the oven to 350F.
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Grease two 9-inch cake pans with 1 tablespoon of butter each.
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Add 2 tablespoons of the flour to each pan and shake the pans to coat the bottom and sides.
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Tap out the excess flour and set the pans aside.
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Sift the remaining 2 1/4 cups of flour with the cocoa, baking powder, baking soda, and salt, and set aside.
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In the bowl of a stand mixer (or in a large bowl if using a hand mixer) cream the remaining butter with the brown sugar, food coloring, and vanilla on low to combine.
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Increase the mixer speed to medium-high and beat until aerated and pale, about 2 minutes.
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Reduce the speed to medium and add the eggs, one at a time, beating thoroughly between each addition and using a rubber spatula to scrape the sides and bottom of the bowl as necessary.
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Reduce the speed to low and add one-third of the dry ingredients followed by half of the buttermilk.
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Repeat, finishing with the final third of the dry mix.
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Scrape down the bottom and sides of the bowl and divide the batter between the two prepared cake pans, spreading it out as evenly as possible.
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Bake until a cake tester inserted into the center comes out clean and the center of the cake resists slight presuure, about 40 minutes.
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Cool on a wire rack for 15 minutes, and then run a paring knife around the edges of each pan to release the cake from the sides; invert the cakes onto the cooling rack.
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Cool for 1 hour, and then wrap each cake in plastic wrap for at least a few hours.
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To Make the Frosting:
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Beat the cream cheese, butter, and vanilla together in the bowl of a stand mixer (or in a large bowl if using a hand mixer) on low speed to combine.
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Increase the speed to medium-high and beat until aerated and light, about 2 minutes.
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Stop the mixer and add a few cups of the confectioners' sugar, incorporating it into the cream cheese mixture on low speed until combined.
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Repeat with the remaining sugar, adding it to the mixer in two additions.
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Once all of the sugar is added, increase the speed to medium-high and beat until fluffy, about 1 minute.
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To Assemble the Cake:
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Unwrap the cake layers.
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Slice off the rounded top 1/8 inch of each cake and place the trimmed-away portion in the bowl of a food processor.
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Slice each cake in half horizontally(you'll end up with 4 layers), working over a baking sheet to catch any crumb.
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Add the crumbs to the food processor and pulse until fine.
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Place one cake layer on a cake round or large plate (make sure that the diameter of the plate is at least 1 inch larger than the cake).
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Use an offset spatula to evenly spread a heaping 3/4 cup of frosting on the first cake layer.
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Repeat with the remaining three cake layers, ending with a bottom half of a cake on top, browned-side up (so you don't get cake crumbs in the frosting).
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Spread the remaining frosting over the top and sides of the cake (the sides dont have to look perfect-you're going to cover them with cake crumbs anyway).
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Gently press a handful of the reserved crumbs into the side of the cake until all of the sides are evenly coated.
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Refrigerate for at least 2 hours before serving.
