Preheat oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper so that it overhangs on two opposite sides. Grease the lining and any exposed pan.
Whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, brown sugar, and sugar until light and fluffy. Mix in the cookie butter.
Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce mixer speed to low. Add the flour mixture in three portions, alternating with two portions of the milk. Mix just until combined or a few streaks of flour remain.
Stir in the chocolate chips.
Transfer the batter to the prepared pan, and spread evenly.
Bake 35 to 40 minutes, or until the edges and top are browned, and a pick inserted into the center comes out clean.
Cool completely in the pan on a wire rack before serving.