Preheat the oven to 350 degrees and grease an 8x8” glass pan well (I used the butter wrapper).
With an electric mixer, cream butter and sugars in a small mixing bowl (if the butter is soft enough, you may be able to do the mixing by hand). Add the egg and vanilla; cream again until smooth. Add the flour, baking soda, and salt. Stir gently until incorporated. Stir in chocolate chips. Store in refrigerator until ready to use.
Cream the cream cheese and sugar together until fluffy (you will probably need an electric mixer to do this properly). Add the egg and vanilla and mix again until well combined.
Press half of the slightly chilled cookie dough into the bottom of the greased pan. Pour the cream cheese mixture on top. To spread cookie dough on top of the cream cheese layer, I rolled the remaining cookie dough into 1-inch balls and then smashed them, and layered the flattened rounds across the surface, then filled in the gaps with any leftover cookie dough. If there are gaps in the cookie dough, remember that the cookie dough will expand in the oven.
Bake for 40 minutes or until the top is set—the center may be a tiny bit jiggly, but not catastrophically so. Check earlier if your oven tends to run hot. Let cool, then cut into tiny squares. Unless, of course, you’re the birthday girl/boy, in which you can take a fork to the pan.