Preheat oven to 350°F. Grease an 8- or 9-inch square baking dish with nonstick spray.
In a large bowl, whisk together flour, granulated sugar, cocoa powder, brown sugar, baking powder, and salt.
In a small saucepan over low heat, combine half of the chopped chocolate and milk. Stir until the chocolate begins to melt. Add butter and continue to stir until fully melted. Remove from heat and mix in vanilla extract.
Pour the chocolate mixture into the dry ingredients. Stir until just combined. Fold in the eggs, remaining chopped chocolate, and 1/4 cup of walnuts.
Transfer the batter to the prepared baking dish. Sprinkle the top with the remaining 1/4 cup walnuts.
Bake for 20–22 minutes for a 9-inch dish or 22–26 minutes for an 8-inch dish, or until a toothpick inserted in the center comes out with moist crumbs. The center should be set but soft. Allow brownies to cool completely in the dish before slicing.