Preheat oven to 350°F. Lightly butter a 9-inch square pan.
In a small bowl, whisk together flour, baking soda and salt; set aside.
In a large mixing bowl, cream together butter, brown sugar and ⅓ cup white sugar. Beat in egg and vanilla.
Add flour mixture, stir by hand to keep from dusting then mix on low speed until well combined. Stir in chocolate chips.
Press half of this dough into bottom of 9-inch square pan.
Roll the remaining cookie dough into an approximately 8 to 9-inch rectangle between 2 sheets of parchment or waxed paper. Set aside and chill briefly while filling is prepared.
For the filling: mix the cream cheese and ⅓ cup sugar until smooth, then blend in vanilla and egg. Pour the filling over cookie dough in the pan.
Cut dough square into smaller 1¼ to 1½-inch squares. Place pieces evenly over the top of the filling. (Cookie layer will expand as it bakes.)
Bake for 25-30 minutes or until golden brown. Let cool completely, and then chill. Cut into squares to serve.