In a saucepan, melt the butter over medium heat. Stir continuously until it foams, turns golden brown, and smells nutty (about 5–7 minutes). Pour into a large mixing bowl and let cool for 10–15 minutes.

To the cooled brown butter, add brown sugar, white sugar, egg, egg yolk, and vanilla. Whisk until the mixture is thick, glossy, and fully combined (1–2 minutes).

In a separate bowl, whisk together the flour, salt, baking soda, and baking powder. Stir the dry ingredients into the wet mixture using a spatula until just combined—don’t overmix.

Gently mix in the crushed graham crackers, graham chunks, and chopped chocolate until evenly distributed.

Using a large cookie scoop, portion the dough into 9 even balls and place on a parchment-lined baking sheet. Press your thumbs into the center of each dough ball to form a shallow “nest.” Place one marshmallow piece in the center, then fold the dough around it—either fully enclosing it or leaving the top slightly exposed.

Cover the baking sheet and chill the cookie dough balls for at least 1 hour (or overnight) to prevent overspreading.

Preheat oven to 350°F (175°C). Line a new baking sheet with parchment paper and space the cold cookie dough balls 2 inches apart. Bake for 10–12 minutes, or until edges are golden and the centers look just set. Cookies may look underdone, but it will continue to set when out of the oven. Let cookies cool on the pan for 5 minutes before transferring to a wire rack to finish cooling.