Place a few graham crackers on a paper towel in the microwave. Place a slightly-damp paper towel on top. Microwave for 15 to 20 seconds, or until the crackers soften enough to cut.
Use a 2-inch circle cookie cutter to cut two circles from each softened graham cracker. Repeat steps one and two with the remaining graham crackers. Let the graham crackers dry.
Spoon a heaping teaspoon or up to a tablespoon of marshmallow crème on each graham cracker circle.
Place the chocolate chips in a microwave-safe bowl. Heat on 70 percent power for 90 seconds and stir well. Continue to microwave at 30 second, then 15 second, intervals just until melted. Stir well.
Place a graham cracker with marshmallow on a fork and hold over the bowl of chocolate. With your other hand, spoon melted chocolate on top, letting the chocolate fall around the sides of the marshmallow and graham cracker. Slide on the prepared baking tray. Repeat with the remaining graham crackers and marshmallows.
Let the cookies set at room temperature for at least an hour, or more quickly in the refrigerator.