For the brownies:
3/4 cup (170 grams) unsalted butter, plus more for the pan
3 ounces (90 grams) bittersweet chocolate, chopped
1 1/2 cups (300 grams) granulated sugar
1 tablespoon vanilla extract
3 large eggs
3/4 teaspoon kosher salt
1/2 teaspoon instant espresso powder (optional)
1/2 cup (40 grams) cocoa powder
1/2 cup (70 grams) all-purpose flour
For the frosting:
6 tablespoons (85 grams) unsalted butter, at room temperature
3/4 cup (100 grams) smooth peanut butter
1/3 cup (40 grams) confectioners’ sugar
1/2 teaspoon flake salt
To make the brownies, preheat the oven to 325°F. Grease an 8-inch square pan. Line the pan with parchment paper so that a couple inches hang over the edge. Then grease the parchment.
Place the butter in a medium saucepan and melt over medium-high heat. Allow the butter to cook until the milk solids bubble up and then settle into the pan and caramelize. Swirl the butter in the pan in order to see the color of the little bits on the bottom. As soon as the milk solids are golden and the butter smells nutty, about 3 to 5 minutes, remove the pan from the heat.
Pour the browned butter into a medium bowl and add the chopped chocolate. Let stand for 1 minute to melt and then whisk together. Whisk in the sugar and vanilla while the butter mixture is still warm. Stir in the eggs, salt, and espresso powder until well blended.
Over the bowl with the chocolate mixture, sift in the cocoa powder and flour. Fold the ingredients together until just combined using a spatula.
Pour the batter into the prepared pan and bake for 25 to 30 minutes, or until a toothpick inserted in the middle pulls out clean. Let cool to room temperature.
To make the frosting, with an electric mixer, whip together the butter, peanut butter, and confectioners’ sugar in a large bowl. Continue to mix until everything is well combined and the frosting has lightened in color. Frost the cooled brownies and finish with the flake salt.
If the brownies are too fudgy to cut, refrigerate for 30 minutes and then cut. Let the brownies sit at room temperature for 10 minutes before serving. Brownies can be made 1 to 3 days in advance. The frosting can be made up to 1 week in advance.