Preheat oven to 350 degrees F.

Brown the butter: Melt butter in a medium sauce pan over medium heat. Continue cooking, swirling the pan occasionally, until the butter stops foaming. Browned bits will start to form at the bottom of the pan and the butter will have a nutty smell, about 5 minutes. Remove from heat and pour into a large bowl. Stir in graham crackers.

Add milk, eggs, vanilla, and bourbon. Whisk to combine.

In a medium bowl, combine flour, sugars, baking powder, baking soda, and salt. Add flour mixture to butter mixture in two additions; mix after each addition until just combined. Fold in chocolate chips.

Pour batter into paper lined muffin tin cups, until ⅔ full. Bake until golden brown, 21 to 24 minutes, or until a toothpick inserted in the center comes out clean.

Cool in pan for 5 minutes, then transfer to a wire rack to cool completely.

Cut top off muffins. Smear a generous dollop of marshmallow fluff on top of the bottom half of the muffin. Put the top back on the muffin; repeat with remaining muffins.