Preheat the oven to 350°F. Line two light-colored baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on medium speed until light and fluffy, about 2 minutes. Add the vanilla and egg, and beat until combined, scraping down the sides of the bowl as needed.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the mixer, mixing on low just until no streaks of flour remain. Fold in the chocolate chips with a spatula.

Arrange 6 graham cracker pieces, 2 chocolate bar rectangles, and 1 marshmallow per cookie on the prepared baking sheets, spacing them about 3 inches apart. Using a large cookie scoop (about 3 tablespoons), portion the dough. Flatten each portion into a disc and place it directly on top of the marshmallow, pressing gently to cover. Sprinkle a few extra chocolate chips on top of each dough disc. Bake for 10 to 13 minutes, until the cookie edges are lightly golden and the marshmallows are puffed and melted.

Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Serve warm or at room temperature.