Combine chocolate cake mix, eggs, vegetable oil, and buttermilk with a stand mixer on low speed. Once combined, up the speed to medium and let the machine go for two minutes. Pour batter into a greased 9x13 pan and bake according to time and temperature on the box.
Remove cake from the oven and begin to prepare pudding by putting both boxes of pudding powder in a medium sized mixing bowl; add the milk. Whisk together just until the lumps are removed, being careful not to over mix. Let mixture sit for 2 minutes to allow it to slightly thicken.
While pudding is setting, poke holes in the cake with the end of a wooden or plastic spoon about an inch apart all over the cake.
Once pudding is ready, spread it directly and evenly over the cake. Gently press it over the holes to help it get down inside of the cake. Allow cake to sit out, uncovered, to cool down. Cover and chill in the fridge till ready to serve. Sprinkle the crushed up Oreo pieces over the entire cake just before serving. Serve chilled.