For the Brownies: Adjust oven rack to middle position and preheat oven to 350°F. Coat a 13- x 9-inch metal baking pan (at least 2 inches deep) with cooking spray. Line with parchment paper, leaving at least 2 inches overhang on two opposite sides to remove brownies from pan. Spray parchment paper with cooking spray. Set pan aside.

In a medium saucepan, melt butter over medium-low heat. Once melted, whisk in granulated sugar and brown sugar until smooth, about 1 minute. Remove from heat and whisk in 1 cup of the chopped chocolate until melted, about 30 seconds. Whisk in cocoa powder, coffee, vanilla, and salt. Let mixture cool for 5 minutes. Working quickly to avoid cooking eggs, add one egg at a time to the chocolate mixture and whisk vigorously after each addition until incorporated. Add flour and ¼ cup of the remaining chopped chocolate, folding until just combined.

Pour brownie mixture into the prepared baking pan, and spread into an even layer. Bake until slightly risen and the top appears somewhat shiny, 30 to 35 minutes.

Remove from oven, and place pan on a wire rack to cool completely, about 1 ½ hours.

For the Peanut Butter Filling: In a large bowl with an electric mixer or in a stand mixer with the whisk attachment, beat butter on medium-high speed until creamy, about 1 minute. Add peanut butter, and beat until light and creamy, about 1 more minute. Gradually add the powdered sugar, ½ cup at a time, and beat until fully incorporated, about 2 minutes, stopping to scrape down sides of bowl as needed. Add heavy cream, vanilla, and salt; beat until combined, about 30 seconds. Dollop peanut butter mixture over cooled brownies, and spread into an even layer. Refrigerate, uncovered, while preparing the chocolate ganache.

For the Chocolate Ganache: In a small heatproof bowl, add chopped chocolate and set aside. In a microwave-safe liquid measuring cup or bowl, microwave cream until hot, but not simmering, 30 to 60 seconds. Add butter to cream, and stir until melted. Pour cream mixture over chocolate in bowl, and let sit for 1 minute. Add kosher salt, and stir until smooth and all chocolate is melted. Remove brownies from refrigerator, and pour the ganache over the peanut butter filling. Use an offset spatula to spread into an even layer. Refrigerate again until chocolate ganache is firm and set, about 1 hour.

Run a sharp knife around the edges of brownies (inside the parchment) to release from the pan. Use the parchment sling handles to remove the brownies from the pan and place on a cutting board. Sprinkle evenly with flaky sea salt. Cut into squares, and serve.