Preheat oven to 350 degrees. Line an 8-or 9-inch square baking pan with parchment paper or foil, allowing some to overhang the sides (this helps remove the bars from the pan).

In a medium bowl, combine the flour, cornstarch, baking powder, baking soda, and salt. Mix well and set aside.

Beat the butter and sugar together until light and fluffy. Beat in eggs, one at a time. Beat in the vanilla. With the mixer on low speed, gradually beat in the flour mixture and mix until blended and smooth, scraping down the sides of the bowl as necessary.

Transfer the dough to the prepared baking pan and press down with water-moistened fingers. Smooth the top with an offset spatula or butter knife.

Bake for 20 to 22 minutes, until the top is golden brown and a wooden pick comes out clean.

Transfer to a wire rack and immediately top with the chocolate chips. Let sit for 2 minutes to allow the chips to soften. After 2 minutes, spread the melted chips over the cookie bars, creating a smooth layer (using an offset spatula works great here).

Cool completely, until the chocolate is set. Don't worry if the center sinks a little; that's normal.