Closely adapted from Baking Bites. If you like your bars gooey in the middle, bake for about 28 minutes on 350 F (330 F convection), or until tops are browned. If you prefer your bars to be more cooked throughout, bake on 325 F (305 F convection) for longer, up to 45 minutes, until top is browned.
Preheat oven to 325 or 350 F (see notes at top to decide which). Line a 9×9-inch square baking pan with parchment paper (lightly spray the corners of the pan to help the paper to stick if necessary). Set aside.
Whisk together flour, baking soda and salt and set aside.
Using an electric beater (I prefer a stand mixer), beat the butter until creamy. Add the sugar and beat. Scrape the sides and bottom of the bowl, and then add the brown sugar. Beat until light and fluffy.
Scrape the sides and bottom of the bowl. Beat in the vanilla and the egg. Scrape the sides and bottom again.
Mix in the flour mixture on the lowest speed. When the flour is mostly but not completely mixed in, add the chocolate chips. Mix until everything is evenly incorporated. Set aside.
Switching to a new bowl (I have 2 bowls and 2 beaters for my stand mixer--if you do not, switch from a stand mixer to a handheld mixer or vice versa or clean your beaters and bowl (after transferring the cookie dough to a clean mixing bowl).
Beat the cream cheese until creamy. Add the sugar and vanilla and beat until well incorporated. Scrape the sides and bottom of the bowl and beat in the egg.
Remove 2 cups of the chocolate chip cookie dough and place it in the prepared pan. Slightly dampen your hands with water and then press the dough into the prepared pan in an even layer.
Scrape the cream cheese mixture into the pan and over the cookie dough base. Shake the pan side to side and front to back briskly, just once or twice, to spread the cream cheese layer.
Drop the remaining cookie dough over the cheesecake layer in tiny broken off blobs. Get it as even as possible.
Bake for 28-33 minutes at 350 F or 38-45 minutes at 325 F (see comments in notes above), until cheesecake is set and cookie dough is golden brown.
Allow to cool completely in the pan, then chill for at least 1 hour before serving.
Use the parchment paper overhangs to lift the entire slab out onto a cutting board. Cut into 16 bars and serve. Store in the fridge in an airtight container.