Place an 8x8-inch baking pan on top of a sheet of parchment paper and trace/outline the pan using a pencil or marker. Turn the parchment paper over (so the ink is on the bottom) and evenly spread the cookie butter inside the square. Transfer the parchment paper to the freezer and chill until firm, about 30 minutes. Note: I recommend checking to make sure the layer is completely firm before starting on the brownie batter!
Preheat the oven to 350°F (180°C). Grease and line the 8x8-inch pan with parchment paper, letting the excess extend over the sides of the pan, then set aside.
Combine the butter, oil, and cocoa powder in a small saucepan over medium-low heat and stir until completely melted, then remove from the heat and set aside.
In the bowl of a stand mixer fitted with the whisk attachment, or in a large bowl using an electric hand mixer, whisk together the granulated sugar and eggs on medium-high until combined and fluffy, about 4-5 minutes.
Add the slightly cooled cocoa mixture and beat until well incorporated.
Add in the flour, baking powder, and salt, and use a rubber spatula to gently fold until just combined.
Pour half of the batter into the prepared baking pan and smooth the top with a spatula. Peel the parchment paper off the frozen cookie butter square and place it on top of the batter.
Pour the rest of the batter on top and spread it evenly to the edges. Bake for 30-35 minutes, or until a toothpick inserted into the center of the brownies comes out fudgy but the edges look cooked through.
Remove from the oven and place on a wire rack to cool completely in the pan before cutting into squares. Cover and store leftover brownies at room temperature for up to 5 days.