Preheat the oven to 375 F and grease donut pans well with butter or nonstick cooking spray that contains flour. In a large bowl, whisk to combine the flour, sugars, cocoa, baking powder, baking soda. Oreo crumbs and salt.
In a medium sized bowl, whisk together the egg, sugars, vanilla, sour cream and melted butter.
Stir the wet ingredients into the dry ingredients until combined.
Use a piping bag or zip lock bag or spoon to fill the dough into the donut molds between ½ and ¾ full.
Bake 8-10 minutes. Place donut pans on a wire rack to cool for five minutes. Turn donuts out onto rack and allow to cool.
Pour the Oreo crumbs into a shallow bowl or dish.
Make the cream cheese icing, chocolate glaze, or vanilla glaze.*
Dip the tops of the donuts in the icing or glaze of your choice. Next, press the tops in the Oreo crumbs or crushed Oreos to coat. Alternatively, you can sprinkle the crumbs or crushed Oreos on top of the donuts. Set donuts on a cooling rack.