Preheat the oven to 350°F (175°C). Line a 9-inch square baking pan with a parchment sling, leaving overhang on two sides for easy removal.
Make the cookie dough: In a large bowl, beat the softened butter, light brown sugar, and 0.25 cup granulated sugar until creamy and slightly lightened, 2–3 minutes. Beat in the egg and 1 tsp vanilla extract until smooth, 30–45 seconds.
In a separate bowl, whisk together 1.25 cups all-purpose flour, baking soda, and 0.25 tsp fine salt. Add the dry ingredients to the butter mixture and mix just until no dry spots remain. Fold in the semisweet chocolate chips. Press the dough evenly into the prepared pan to form a level base.
Make the brownie batter: In a medium bowl, whisk the melted butter and unsweetened cocoa powder until glossy. Whisk in 1 cup granulated sugar until evenly combined. Whisk in the eggs one at a time until the mixture is thick and shiny, then whisk in the remaining 1 tsp vanilla extract and remaining 0.25 tsp fine salt.
Sprinkle the 0.75 cup all-purpose flour over the batter and fold with a spatula just until no flour streaks remain; do not overmix. Spoon the brownie batter over the cookie layer and gently spread to the edges to cover without disturbing the base.
Bake until the top is set, the edges are slightly pulled away from the pan, and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter), 35–40 minutes.
Cool the pan on a wire rack until completely cool, about 1 hour. Lift out using the parchment, cut into 16 squares, and serve.