Preheat oven to 350°F and line a metal 9×13-inch cake pan with parchment paper and spray lightly with cooking spray. Make sure some of the parchment is over the edge of the pan for easy removal. This may require two sheets, one going in each direction – make sure the one that goes across the shorter distance is under the one that goes along the full length of the pan.
Melt 1 cup salted butter in a heavy-bottomed saucepan over low heat. Add 2½ cups granulated sugar and stir until smooth, the butter and sugar have started emulsifying, and no butter is separated from the sugar. Remove from heat and let the mixture cool for 5 minutes, stirring often to release heat.
Add 2 tablespoons canola oil and 1 tablespoon vanilla extract to the butter and sugar and beat them in with a rubber spatula until fully combined and there's no separation between the ingredients (no oil resting on top).
Beat in 5 large eggs one at a time, beating with the spatula or a fork after each one. Mix until fully incorporated.
Sift 1 cup all-purpose flour, ½ cup unsweetened cocoa powder, ⅓ cup black cocoa powder, and ¾ teaspoon salt into the butter and sugar mixture, stirring gently with a rubber spatula just until the dry streaks are gone.
Chop up 9 of the 12 Double Stuf Oreos and add them to the brownie batter. Chop up the remaining 3 Oreos and set aside.
Chop up the 8 ounces milk chocolate and add most of it into the batter.
Pour the brownie batter into the prepared baking pan, sprinkle the remaining chocolate chunks and Oreo pieces on top, and bake for 28 to 32 minutes.
Cool completely before removing it from the pan and slicing it for best results. Use a plastic knife for the cleanest cuts.