For the cookie dough: With an electric mixer, cream butter and sugars in a small mixing bowl. Add vanilla and egg; 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.
Preheat oven to 350 degrees F (175 degrees C). Prepare brownie batter as directed on the box. Pour batter into a greased 8x8 or 9x9 inch baking dish. Scatter pieces of cookie dough over the top of the brownie batter. Gently press the cookie dough into the batter.
Bake for 35-40 minutes, or until the edges are set and a toothpick inserted near the center comes out with moist crumbs attached. Let stand for 15-20 minutes before cutting into squares.
Notes
Adjust baking time based on your desired level of gooeyness. For a more fudgy brownie, bake for the shorter end of the time range. For a more cake-like brownie, bake longer.