Preheat the oven to 350°F and line a 9x9-inch baking pan with parchment, leaving an overhang on two sides.
Beat the butter, brown sugar and granulated sugar until light and fluffy, about 2 minutes. Beat in the egg yolk and vanilla, then stir in the flour, baking soda and salt until a soft dough forms. Fold in the chocolate chips.
Press about two thirds of the cookie dough evenly into the bottom of the pan and bake for 10 minutes. Reduce the oven to 325°F and set the remaining dough aside.
Blend the cottage cheese in a food processor or blender for 2 to 3 minutes, scraping down the sides, until completely silky. Add the cream cheese, sugar, cornstarch and vanilla and blend until smooth, then pulse in the eggs just until combined.
Pour the cheesecake batter over the warm cookie base. Pinch the remaining cookie dough into small pieces and scatter them over the top.
Bake for 40 to 45 minutes, until the cookie pieces are golden and the center has a slight wobble.
Cool completely in the pan, then refrigerate for at least 4 hours. Lift out using the parchment and cut into 16 bars.