Line an 18×13-inch rimmed baking sheet with parchment, leaving a little overhang on the long sides for easy lifting. Lightly grease the parchment and exposed pan.
In a medium bowl, whisk together the flour, cornstarch, baking soda, and fine sea salt; set aside.
In a stand mixer fitted with the paddle (or using a hand mixer), beat the softened butter with the brown sugar and granulated sugar on medium speed until light and creamy, 2 to 3 minutes. Add the cream cheese and continue beating until fluffy and fully blended, about 1 minute more.
Beat in the eggs one at a time, then mix in the vanilla just until combined. Scrape down the bowl.
Add the dry ingredients in two additions on low speed, mixing only until the flour disappears. Fold in about 1 3/4 cups of the chocolate chips, reserving the rest for topping.
Scrape the dough onto the prepared sheet pan and spread into an even layer with an offset spatula. Scatter the reserved chocolate chips over the top and gently press them in. Place the pan in the refrigerator for 10 minutes to help the bars bake with neatly defined edges.
While the dough chills, heat the oven to 325°F (163°C). Bake the cookie bars for 24 to 28 minutes, rotating the pan once halfway through, until the edges are golden and the center looks set but still slightly soft.
Set the pan on a rack, sprinkle lightly with flaky sea salt, and cool for 20 minutes. Lift the slab out using the parchment overhang and cool completely before slicing into 30 bars.