Preheat the oven to 325°F and grease an 8x8, 9x9 or 9x13-inch baking pan. (see recipe notes for baking times for the different sized pans).
Make the cookie dough first. In a large bowl, whisk together the all-purpose flour, cornstarch, baking soda, baking powder and salt. Set aside.
Cream the butter and sugars in a stand mixer using the paddle attachment until light and fluffy, ~2-3 minutes. Add in the egg, egg yolk and vanilla extract. Gradually add in the dry ingredients. Add in chocolate chips just until combined.
Make the cheesecake filling: using a hand mixer, beat the cream cheese and sugar until light and fluffy. Add in the egg, vanilla and flour and mix again until incorporated and smooth.
With lightly floured fingers, press ~2/3 of the cookie dough down onto the bottom of the prepared pan. (Note: It will be a pretty thin layer if using a 9x13 inch pan).
Pour the cheesecake filling over the crust in an even layer. Take remaining cookie dough, flatten into discs and place on top of cheesecake layer. Repeat until cheesecake layer is mostly covered with cookie dough (there will be some gaps, that's OK).
Bake for ~30-40 minutes* or until cheesecake layer appears set. Cool for at least 45 minutes at room temperature before cutting into bars. (In the recipe video it notes to chill bars in fridge, but that's not completely necessary. We've dug into these bars before chilling and they were perfect. Chilling just ensures clean cuts in the bars!)
When ready to serve, let stand at room temperature for 15 minutes or so before serving for the cookie to soften. Cut into small squares. Store in an air-tight container in the fridge.