Preheat the oven to 350°. Grease a 9 x 9-inch baking pan with non-stick cooking spray.
In a large, microwave-safe bowl melt the butter. Add the sugar and chocolate chips to the butter and stir until smooth and silky. (The heat of the butter should melt the chocolate. If it doesn't microwave at 20-second intervals and stir in between.)
Allow this mixture to cool.
While that is cooling, whisk together both cocoa powders, flour, and salt in a separate bowl.
Beat the eggs then add them and the vanilla extract to the cooled butter mixture. Stir well.
Stir in the dry ingredients and fold the mixture gently until well mixed. There may still be small, dry clumps and that's ok. Don't over mix the batter. It will be thick.
Pour the batter into the prepared baking pan and bake for about 35-40 minutes. The top may crack if it does it's okay, you'll cover it with frosting.
Let the brownies cool before frosting them.
Cream the butter and shortening with the whisk attachment of an electric mixer until light and fluffy.
With the mixer on low add the powdered sugar. Mix until incorporated.
Add 1 tablespoon whipping cream and vanilla extract and mix. Add the other tablespoon of whipping cream if needed. You want the mixture to be soft and fluffy.
Fold in the crushed Oreo by hand until evenly incorporated.
Spread frosting carefully and evenly over the brownies with an offset spatula.
Serve. Store leftovers in an airtight container on the counter. They'll stay fresh 4 to 5 days in an airtight container.