Preheat the oven to 350°F. Grease and line two 8-inch round cake pans with parchment; lightly dust with flour or cocoa and tap out the excess.
In a large bowl, sift together the flour, cocoa powder, baking powder, baking soda, salt, and instant espresso powder. Whisk briefly to blend and set aside.
In a separate bowl, whisk the buttermilk, sour cream, oil, eggs, vinegar, vanilla, and red gel coloring until smooth and evenly colored.
Make a well in the dry ingredients and pour in the wet mixture. Using a rubber spatula, fold the batter gently until just combined — avoid overmixing. The batter will be thick and slightly glossy.
Fold in the coarsely chopped Oreos by hand so they stay chunky and distributed; reserve a few pieces for decorating. Divide the batter evenly between the prepared pans (use a kitchen scale or scoop for even layers).
Bake on the center rack for 30–35 minutes, or until a toothpick comes out with just a few moist crumbs. Rotate the pans halfway through baking for even browning.
Let the cakes cool in the pans for 15 minutes, then run a knife around the edges, invert onto a wire rack, peel off parchment, and cool completely before frosting (cooling fully helps the frosting hold).
While the layers cool, make the frosting: beat the softened cream cheese and butter together on medium speed until very smooth and slightly aerated (about 2–3 minutes).
With the mixer on low, add the powdered sugar one cup at a time until incorporated, then increase speed briefly to reach a spreadable consistency. Taste and adjust sweetness if needed.
Fold in the finely crushed Oreos with a spatula so the frosting keeps a slightly speckled texture. Chill the frosting in the refrigerator for 20–30 minutes if it seems too soft to spread.
Place one cake layer (flat side up) on a cake plate. Spread about a third of the frosting evenly over the top. Stack the second layer and press gently to level.
Apply a thin crumb coat of frosting all over the cake to seal in crumbs. Refrigerate the cake for 30 minutes to firm the crumb coat.
Finish with a generous second layer of frosting, smooth with an offset spatula, and decorate with reserved Oreo pieces or halves. Chill 20–30 minutes before slicing to make clean slices.