Preheat the oven to 350°F. Line 2 baking sheets with parchment paper, or coat them lightly with nonstick spray.
Whisk 3 cups all-purpose flour, 2 teaspoons baking soda, and 1 teaspoon salt together in a medium bowl.
Beat 1 cup room-temperature unsalted butter, 1 cup firmly packed light brown sugar, and 3/4 cup granulated sugar at medium speed until smooth and creamy.
Mix 2 large eggs and 2 teaspoons vanilla extract into the butter mixture on low speed until incorporated.
Gradually mix the 3-cup flour mixture into the wet ingredients just until combined. If the dough is too soft to hold a mound, add 2 to 4 tablespoons additional flour, 1 tablespoon at a time.
Gently fold 2 to 3 cups cold brownie chunks into the cookie dough just until distributed.
Use a 1/4-cup scoop to make 20 large dough portions. Place 6 to 8 portions on each prepared baking sheet with plenty of room between them.
Chill the 20 scooped dough portions for 15 to 30 minutes, or flash-freeze them for 10 minutes, for extra-thick cookies.
Bake 1 sheet at a time at 350°F for 12 to 14 minutes, until the bottoms and edges are lightly browned and the tops feel firm when lightly touched.
Immediately press approximately 1/2 cup chocolate chips, as needed, onto the warm cookie tops. Rest the cookies on the baking sheet for 5 minutes, then transfer them to a wire rack to cool.