Preheat your oven to 350°F (177°C). Line an 8-inch or 9-inch square baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out once cooled. Set aside.
In a large mixing bowl, using a hand mixer or a stand mixer fitted with the paddle attachment, cream together the softened butter and brown sugar on medium-high speed for about 2 minutes until light and fluffy. Add the egg and vanilla extract, then beat until fully combined. Scrape down the sides and bottom of the bowl as needed—the mixture may look slightly curdled at this stage, which is completely normal.
In a separate bowl, whisk together the flour, graham cracker crumbs, baking powder, and salt. Add the dry ingredients to the wet mixture and mix on medium speed until fully incorporated. The dough will be soft and sticky.
Press about two-thirds of the graham cracker cookie dough into the bottom of your prepared pan. It will be a thin layer—use your hands or a spatula to help spread it evenly. Next, gently spread the marshmallow creme over the dough. It may be sticky and difficult to handle, so take your time to smooth it out as evenly as possible. Sprinkle the chocolate chips evenly over the marshmallow layer.
Take the remaining cookie dough, flatten it into small pieces with your hands, and arrange it over the top of the chocolate chips. Don’t worry about fully covering the surface—some of the chocolate and marshmallow can peek through.
Bake the bars for 25 to 30 minutes, or until the top is lightly golden brown. Remove from the oven and place the pan on a wire rack to cool completely.
Once fully cooled, lift the bars out of the pan using the parchment overhang and slice into squares. Store leftovers covered at room temperature for up to one week.