I ate more than one brownie trying to decide if I could specifically discern the nuttiness of the browned butter. In certain bites, I convinced myself I had, but it may have just been an excuse to eat more brownies. Even if the brown butter doesn't completely come through, it absolutely adds to the richness of the brownie, and the taste and texture are both great. I still hate nuts in chocolate, so I replaced the walnuts with chocolate chips. You can see the chunks below. It's never a mistake to add more chocolate.
Bon Appetit makes the bold claim that these are the best brownies ever. I don't know if that's quite true, but they are certainly very good and I will definitely try them again soon. (Besides, they're easy, and I love the smell of browned butter.)
Cocoa Brownies with Browned Butter
Adapted from The Cilantropist, adapted from Bon Appetit, February 2011
1 1/4 sticks (10 tablespoons) unsalted butter, cut into 1" pieces
1 1/4 cups (8 3/4 ounces) sugar
3/4 cups (2 1/4 ounces) cocoa powder
1 teaspoon vanilla
1/2 teaspoon sea salt
2 teaspoons water
1/3 cup plus 1 tablespoon (1 3/8 ounces plus 1 tablespoon) flour
1 cup chocolate chips (or chopped nuts, if you must)
extra sea salt for sprinkling (optional)
Preheat oven to 325F. Line an 8" square pan with tinfoil, leaving 2" overhangs and pressing the foil tightly to the sides of the pan. Spray lightly with cooking spray.
In a large saucepan - preferably not an nonstick saucepan, since you won't be able to see the color of the butter - melt the butter over medium heat, stirring often. It will melt, then foam, and then form more clear bubbles. Once the foam has subsided and there are brown bits at the bottom of the pan, remove the butter from the heat. Stir in the sugar, cocoa powder, vanilla, salt, and water. Let cool for 4-5 minutes, and then mix in the eggs, one at a time, beating quickly (with a spoon) after each addition. When the mixture looks smooth, stir in the flour and mix well. Stir in the chocolate chips. Transfer to the prepared pan and smooth the top before baking.
Bake for 28-30 minutes (or it could take a little longer) until a toothpick inserted in the center comes out almost clean. Remove the pan from the oven and cool completely. Then remove the brownies from the pan, pull away the tinfoil, and cut into squares. Store in an airtight container. They freeze well, too.