Preheat the oven to 325°F. Grease an 8 inch or 9 inch square baking pan.
Brown the butter by heating it on medium-low in a small pot. The butter will melt and bubble. Turn off the heat when the bubbling stops. The butter should have darkened and smell slightly nutty. Remove from heat and let cool slightly.
⅔ cup (5.3 ounces or 151 grams) unsalted butter
Pulverize the graham crackers in a food processor or by hand and add it to a medium bowl.
6 whole graham crackers (or 3.2 ounces or 90 grams graham cracker crumbs)
Sift the flour, salt, baking powder, and baking soda into the bowl with the graham crackers and whisk to mix.
⅖ cup (3.0 ounces or 83 grams) bleached all-purpose flour, ½ teaspoon salt, ½ teaspoon baking powder, ¼ teaspoon baking soda
In the bowl of a stand mixer (or another medium bowl if using a hand mixer or mixing by hand), combine the sugar and brown butter.
½ cup (3.4 ounces or 96 grams) dark brown sugar
Add in the egg and egg yolk and beat on medium speed for one minute.
1 large egg, 1 egg yolk
Add the vanilla and beat on medium speed for one minute.
½ teaspoon vanilla extract
Stir in the dry ingredients by hand and then add the chocolate chips and mix.
8 ounces semisweet or bittersweet chocolate chips
Spread the mixture evenly in the prepared pan and bake for 30-35 minutes, until the bars start to brown and pull away from the sides of the pan, a toothpick inserted in the middle comes out clean, and the cookie feels somewhat firm.
Take the pan out of the oven and set the oven to broil with a rack 6 to 8 inches from the broiler.
While the broiler is heating, add the graham cracker pieces and then the mini marshmallows to the pan.
2 whole graham crackers, broken into pieces, ½ cup mini marshmallows
Broil for 45 to 60 seconds, watching closely, until the marshmallows have achieved your ideal brownness.
Remove from the oven, sprinkle on the chocolate chips, and cover with foil for 5 to 10 minutes.
4 ounces semisweet or bittersweet chocolate chips
These chocolate chip marshmallow cookie bars can be stored at room temperature for up to one week.