Preheat your oven to 350°F (175°C) and prepare the baking dish by greasing it with butter or using parchment paper.

In a medium saucepan, combine 1.5 sticks of unsalted butter and 6 oz of espresso over low to medium heat. Stir gently until fully melted, about 5 minutes.

Add 0.5 cups of cocoa powder and 3.5 oz of chopped dark chocolate to the melted mixture. Stir until melted and smooth, about 2-3 minutes.

In a large mixing bowl, whisk together 1.25 cups of light brown sugar, 0.5 tsp of kosher salt, and 0.5 tbsp of bourbon vanilla extract until well incorporated.

Pour the slightly cooled chocolate mixture into the bowl with dry ingredients. Stir until smooth, about 2 minutes.

Add 3 large eggs and 2 egg yolks to the mixture. Whisk until combined, about 1-2 minutes.

Gently fold in 1 cup of all-purpose flour and 0.5 tbsp of baking soda. Mix until just combined.

Pour the batter into the prepared baking dish and bake for 22-25 minutes, or until a toothpick in the center comes out clean.

Remove the cake from the oven and cool in the dish for about 15-20 minutes before transferring to a wire rack.

Melt 1 stick of unsalted butter in a saucepan over low to medium heat until golden brown and nutty, about 5-7 minutes. Transfer to a bowl to cool.

In a mixing bowl, combine the cooled brown butter with 4 cups of powdered sugar. Gradually whisk in 0.5 tbsp of vanilla extract, 0.5 tsp of kosher salt, and 3 tbsp of cold heavy cream until smooth.

Once the cake has cooled completely, spread the brown butter frosting evenly over the top.