Preheat The Oven & Prep Your Pan. Start by preheating the oven to 325 degrees F. Line an 8x8 square metal baking pan with parchment paper. (Stick with a metal pan, as a glass pan will cause the brownies to bake longer and climb the sides)
Melt Chocolate & Butter. Add the butter and 2/3 cup chocolate chips to a saucepan and melt on low heat until smooth. (Or, add them to a microwave-safe bowl and melt in 20-second increments until smooth.) Set the melted chocolate mixture aside to cool while you mix the eggs and sugar.
Dissolve The Sugar. Next, add the sugar, eggs, and egg yolk to a large mixing bowl. Whisk or beat the sugar and eggs with a hand mixer until the sugar is dissolved and the mixture is light yellow. (There should be VERY little grit when you rub the sugar/egg mixture between your fingers.)
Combine. Gradually mix the melted chocolate mixture into the eggs and sugar mixture until well blended. Mix in the vanilla.
Add Dry Ingredients. Then, add the flour, cocoa power, and salt to the brownie batter. Gently fold the dry ingredients in with a spatula until just a few floury patches remain. Add the next 2/3 cup chocolate chips and fold in until the brownie batter is just combined.
Layer The Brownies. Pour half of the brownie batter into the prepared baking pan. Add 16 gluten-free Oreos in a single layer over the batter. Cover the oreo layer with the second half of the brownie batter. Chop up the remaining 8 Oreos and add them to the top of the brownies.
Bake & Cool. Pop the brownies in the oven and bake 25-30 minutes, or until the top is set and shiny, and a toothpick inserted in the center has some fudgy brownie on it. (If it comes out clean, the brownies are over-cooked. If it comes out with liquid brownie batter, the brownies aren't done yet.) Mine are usually done around 27-28 minutes. The brownies will continue to set as they cool. Set the brownies on a wire rack to cool completely. For the neatest cuts, chill the brownies in the fridge after they're cooled before cutting them into squares.
Serve & Store. Cut the brownies into squares or rectangles and enjoy right away. Store leftover brownies in an airtight container at room temperature 2-3 days, or in the freezer up to 2 months. Keep in mind that these brownies will cut best when they're completely cooled (even better if they're chilled!) Chilling the brownies before cutting them will give you beautiful, clean cuts without pushing the Oreos down into the brownies.