Heat the oven to 350°F. Coat an 8x8-inch square baking pan with cooking spray. Line the pan with 2 sheets of parchment paper, positioning them perpendicular to each other and making sure they are long enough to hang over the edges by at least 2 inches to form a sling.

Beat 6 tablespoons room-temperature unsalted butter, ⅔ cup granulated sugar, and ¼ teaspoon kosher salt together in a stand mixer with the paddle attachment on medium speed until light and fluffy, about 2 minutes.

Reduce the speed to low. Add 1 room-temperature large egg and 1 teaspoon vanilla extract, and beat until combined, scraping down the sides of the bowl with a flexible spatula as needed.

Turn the mixer off. Add 1 cup all-purpose flour and sprinkle the surface with ¾ teaspoon baking powder. Beat on medium speed until just combined and the texture of thick cake batter.

Transfer the dough to the baking pan and spread into a smooth, even layer. Sprinkle ⅔ cup semi-sweet chocolate chips and ½ cup miniature marshmallows evenly over the top.

Wash and dry the stand mixer bowl. Beat 2 room-temperature large egg whites, ⅔ cup packed brown sugar, ¼ teaspoon vanilla extract, and 1 pinch kosher salt together in the stand mixer with the whisk attachment on high speed until medium, shiny peaks form, 4 to 5 minutes. Transfer onto the cookie base and spread into an even layer.

Bake until golden-brown and the top begins to crack, 28 to 30 minutes.

Place on a wire rack and let cool until just warm or at room temperature, at least 1 hour. Grasping the excess parchment, lift the slab out of the pan and place on a cutting board. Cut into 9 pieces; for the cleanest-looking slices, wash the knife and wipe dry between cuts.