How to Make It
Whisk together flour, cracker crumbs, baking powder, salt, and baking soda in a medium bowl. Set aside.
Beat together butter, brown sugar, and granulated sugar with a stand mixer at medium-high speed until very light and fluffy, about 5 minutes. Add eggs, 1 at a time, beating to incorporate. After adding both eggs, continue to beat until very whipped, 3 to 4 minutes. Add vanilla.
Reduce speed to low, and gradually add flour mixture to butter mixture. Beat until combined, about 10 seconds.
Scoop cookies with a 1 1/2-inch scoop about 2 inches apart onto a baking sheet lined with parchment paper. Flatten cookies slightly, and press a chocolate piece into each cookie. Top each with a halved marshmallow. Cover baking sheets with plastic wrap, and chill at least 24 hours, and up to 48 hours (or alternatively, freeze about 15 minutes).
Preheat a convection oven to 450°F (or a conventional oven to 425°F). Bake cookies in preheated oven on lined baking sheets until puffed and golden and marshmallow is browned, about 7 minutes. Let cookies stand about 5 minutes before transferring to a wire rack to cool until set, about 5 more minutes.