Preheat oven to 350 degrees F and lightly spray two donut pans with baking spray. Set aside.
Combine cocoa powder, flour, brown sugar, baking powder, baking soda, salt, and chocolate morsels in a large bowl and whisk.
In a 4-qt liquid measuring cup or a medium bowl, combine eggs, milk, vanilla extract, and vinegar and whisk.
Pour wet mixture and melted butter into the bowl with the dry ingredients and beat until combined.
Divide batter between the donut pans and bake for about 15 minutes, until set.
While donuts are baking, prepare the icing by beating together the butter, Crisco, powdered sugar, and vanilla extract.
Add in the milk, a little bit at a time, beating after each addition.
Open the Oreos and scrape off the cream filling and crush the cookie wafers .
Once donuts are cooled, dip into the icing and sprinkle with crushed Oreos.