Preheat the oven to 350°F; position the rack in the middle of the oven. Line three rimmed baking sheets with baking mats or parchment paper.
In a large bowl, whisk together the flour, graham cracker crumbs, baking soda, and salt until thoroughly combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and both sugars together on medium speed until light and fluffy. Meanwhile, in a small bowl, lightly beat together the egg, maple syrup, and vanilla. Add the egg mixture to the whipped butter-sugar mixture and mix until combined.
Add the flour mixture and mix on low speed until combined. Fold in the chocolate chips. Scoop golf ball–sized balls of the dough and place them on the prepared pans, leaving 2 inches between the cookies on all sides. (You should be able to fit 6 cookies on each half-sheet at a time.) Bake for about 5 minutes, or until the cookies start to spread. Remove the pans from the oven and place 4 marshmallows on top of each cookie, gently pressing them into the dough. Return the cookies to the oven and bake for 10 minutes more, or until the cookies are golden and set around the edges and still a little soft in the center. Transfer the cookies to a wire rack and let cool completely. Store the cookies at room temperature in a tightly sealed container for up to 1 week.