Prepare the Baking Pan: Preheat your oven to 350°F (175°C). Line an 8×8-inch square pan with parchment paper, lightly spraying the pan with non-stick spray to ensure the paper sticks.
Brown the Butter:
In a medium saucepan, melt the unsalted butter over low heat. Once fully melted, increase the heat to medium-low. Stir occasionally. The butter will begin to foam and crackle before browning. Keep an eye on it as it can burn quickly.
Once the butter has browned and has a nutty aroma, remove from the heat and pour into a heatproof bowl. Allow it to cool to room temperature.
Make the Brownie Batter:
In a small bowl, whisk together flour, cocoa powder, baking powder, salt, and espresso powder (optional).
In a separate saucepan, melt the butter and unsweetened chocolate over low heat. Remove from heat and let cool slightly.
Stir in the granulated sugar, light brown sugar, egg, and vanilla extract.
Gradually add the dry ingredients into the wet ingredients, stirring until combined.
Optional: Fold in the miniature marshmallows for added fudginess.
Spread the brownie batter into the prepared pan and set aside.
Make the Cookie Dough Layer:
In a small bowl, whisk together flour, baking powder, baking soda, and salt.
In the bowl with the cooled brown butter, add the granulated sugar and light brown sugar, and beat until smooth.
Add the egg, milk, and vanilla extract. Mix until incorporated.
Fold in the dry ingredients until fully combined.
Stir in ¾ of the chocolate chips.
Spread or dollop the cookie dough over the brownie batter. Sprinkle the remaining chocolate chips on top and lightly sprinkle with flaky sea salt.
Bake and Cool:
Bake in the preheated oven for 35-38 minutes. The bars should be lightly golden on top. A toothpick inserted should come out with just a few moist crumbs.
Let the Brown Butter Brookies cool completely in the pan before cutting into squares.