Pulse the Oreo cookies in a food processor to fine crumbs; sift out any large pieces and set aside. Reserve 6–8 whole cookies (or halves) for decorating the top later.
Make the frosting base first so it can set: In a stand mixer fitted with the paddle, beat the butter on medium-high until very pale and fluffy, 3–4 minutes. Add half the powdered sugar, the milk powder (if using), and a pinch of salt; mix on low to incorporate, then beat on medium for 45 seconds. Add the remaining sugar and 4 tablespoons heavy cream plus vanilla; beat until smooth and spreadable, adding more cream 1 teaspoon at a time if needed. Fold in about 2/3 of the Oreo crumbs by hand to keep the frosting speckled rather than gray. Cover and refrigerate 20 minutes.
Preheat the oven to 325°F (165°C). Line three 8-inch round cake pans with parchment, grease the sides, and dust lightly with cocoa powder (tap out excess).
Bloom the cocoa: In a heatproof bowl, whisk the Dutch-process cocoa and black cocoa with 1/2 cup of the hot coffee until smooth and glossy; let stand 5 minutes. Whisk in the remaining 1/2 cup hot coffee.
In a large bowl, whisk together flour, granulated sugar, brown sugar, baking powder, baking soda, and salt until evenly combined.
Add oil, eggs, sour cream, and vanilla to the dry mixture. Beat with a hand mixer (or the stand mixer with paddle) on medium speed just until a thick, smooth paste forms, about 30–45 seconds. Scrape bowl and beater.
Stream in the warm cocoa-coffee mixture on low speed until fully incorporated; the batter will be pourable. Let the batter rest 10 minutes to allow the cocoa to bloom further and bubbles to settle.
Divide batter evenly among the prepared pans (about 1 2/3 cups per pan). Bake at 325°F for 24–28 minutes, until the centers spring back lightly and a toothpick comes out with a few moist crumbs.
Cool cakes in pans 10 minutes, then turn out onto wire racks, peel parchment, and cool completely. For easiest assembly, chill layers for 20 minutes after cooling.
Level the tops if needed. Place the first layer on a board. Transfer about half the frosting to a piping bag fitted with a large round tip (or snip a 3/4-inch opening). Pipe a thick ring around the edge to create a dam, spread a thin layer inside the ring, and sprinkle 1–2 tablespoons of the reserved plain Oreo crumbs over the center. Top with the second layer and repeat. Place the third layer upside down for the flattest top.
Apply a thin crumb coat over the top and sides, filling any gaps. Chill the cake for 15 minutes to set.
Finish with a thicker coat of frosting. Press remaining fine Oreo crumbs up the sides to form a crumb-collar. Pipe rosettes on top with an open star tip and nestle reserved Oreo halves into the swirls. Slice with a warm, dry knife for clean edges.