Preheat oven to 350° F. Line an 8-inch by 8-inch pan with parchment paper. Set aside.
Brown butter. In a medium or large size saucepan, melt the butter over the lowest possible heat. Once it is fully melted, increase the heat to medium-low. The butter will start popping and crackling and then start foaming. The part of the butter that will start browning is the milk solids which will be on the bottom of the pan. This is why you should keep stirring with a heatproof spatula or wooden spoon, lifting it to see what stage the browning is at. Once you have nicely browned specks on the bottom of the pan, remove the pan from the heat and immediately pour the butter into a medium, heatproof mixing bowl to stop it from cooking any further. (Be careful not to overcook the butter. It can go from brown to burnt very quickly.) Allow the butter to cool to room temperature. Set the bowl of browned butter aside for the brown butter cookie dough in Step 9.
Brownie batter. In a small bowl, whisk together the flour, cocoa powder, baking powder, salt and espresso powder. Set aside.
In a small saucepan, melt butter and chocolate over the lowest possible heat. Set aside for a few minutes to cool slightly.
Stir in sugar and brown sugar. Beat in egg and vanilla.
Gently mix the dry ingredients into the wet ingredients, just until the flour is fully absorbed. Stir in miniature marshmallows, if using.
Spread brownie batter into prepared pan and set aside.
Brown butter cookie dough batter. In a small bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
Into the bowl of cooled browned butter, mix in the sugars, then beat in the egg, milk and the vanilla extract.
Fold the dry ingredients into the wet, just until the flour is fully absorbed. Fold in 128 grams (3/4 cup) of chocolate chips.
Spread or dollop the cookie batter over the brownie batter. Sprinkle the top with the remaining chocolate chips. Sprinkle with flaky sea salt.
Bake for 35-38 minutes. A toothpick inserted should come out just barely wet. Allow to cool completely in pan.