Grease an 8x8 inch square baking pan with butter, then line with parchment paper. There should be overhang on the sides, so that it is easy to remove the bars when they are finished.
On the stovetop, set a light-colored sauce pan to medium heat. Add cubed unsalted butter, and melt until fragrant and browned in color, stirring continously. Transfer immediately to a heat-proof bowl, and set aside to cool slightly.
Preheat the oven to 325 degrees Farenheit.
Add flour and baking soda to a medium-sized mixing bowl. Whisk them together until combined.
In a large mixing bowl, add cookie butter, salt, dark brown sugar, granulated sugar, and vanilla extract, then pour in the cooled brown butter. Use a spatula to cream the ingredients together, folding and stirring until everything is combined. The mixture will be dark in color.
Next, gently fold in the two eggs, until just combined. Now, add the egg yolk, and stir until just combined. Be careful not to overbeat the eggs.
Sift the dry ingredients into the wet ingredients. Use your spatula to gently fold in the dry ingredients until they are just combined with the wet ingredients. Do not overmix the batter; stop as soon as everything is combined. The batter will be very thick, almost like a slightly liquidy cookie dough.
Now, gently fold in the chocolate chips.
Pour the batter into the prepared baking pan and bake in the preheated oven for 30-34 minutes. Start checking the bars after 25 minutes, in the oven. They are finished when the edges are golden brown and the center looks mostly set. A toothpick inserted in the center will come out mostly clean, with a few wet crumbs. The center may look a little underdone, but it will set more as it cools.
Remove the bars from the oven and set them on a cooling rack to cool for about an hour. Use the parchment paper to carefully remove the bars from the pan; slice them into squares.
Serve warm and enjoy!