Using a stand or hand mixer, beat butter and sugars in a bowl until creamy, about 2 minutes. Beat in egg and vanilla until combined.
In a separate bowl, stir together flour, salt, baking powder, and baking soda. Gradually add flour mixture to butter mixture, beating on low speed until just combined.
Fold in both chocolates and oats until just combined (do not overbeat).
Divide dough in half; spread half of dough in an even layer in the bottom of a foil-lined, greased 9x9-inch baking pan. Set pan aside while making brownie layer.
Refrigerate remaining dough for 15 minutes; reserve for additional cookies (see note below).
Make the Cookie Layer:
Place the Oreos on top of the cookie dough layer; breaking cookies to fit, as needed.
Make the Brownie Layer:
Preheat oven to 350°F. Mix the cocoa powder, flour, espresso powder, and baking powder in a bowl then set aside.
In a medium bowl, beat together melted butter, sugars, eggs, and vanilla. Mix very well as this step gives you that nice brownie top.
Sift the dry mixture into the butter mixture; stir until no streaks remain then fold in the chocolate chips.
Pour brownie batter over Oreo layer; gently smooth top with an offset spatula.
Bake at 350° until a wooden pick inserted comes out mostly clean, 35 to 40 minutes.
For best slicing results, let cool completely, about 2 hours.
Using foil as handles, lift brownies from pan. Discard foil; cut brownies into desired shapes.
Store in an airtight container up to 3 days, or refrigerate up to 1 week, if you can resist them that long!
Video
Notes
Don’t stress about making a solid layer with the Oreo cookies; you can fill in some gaps with caramel-filled chocolates or more broken Oreos, and the brownie batter will handle the rest. -Use any blend of chocolate that you desire for the cookies and the brownies. I’m a big fan of dark chocolate, but feel free to sneak some milk chocolate in, if that floats your boat. -It’s going to be very hard to resist eating these hot out of the pan, but they do slice best when allowed to cool for a couple of hours. I like to cut them into nine even squares, then cut the squares diagonally into triangles.