MICROWAVE 2/3 cup chunks in small, uncovered, microwave-safe bowl on HIGH (100%) power for 45 seconds; STIR. If chunks retain some of its original shape, microwave at additional 10- to 15-second intervals, stirring just until melted. Cool to room temperature.
COMBINE flour, cocoa, baking soda and salt in medium bowl. Beat butter, brown sugar and granulated sugar in large mixer bowl until creamy. Beat in melted chocolate. Add egg and vanilla extract, mixing until well blended, about 1 minute. Add flour mixture, mixing just until blended. Stir in graham cracker pieces and 1/2 cup chunks. Refrigerate for 1 hour.
PREHEAT oven to 325º F. Line baking sheets with parchment paper.
SHAPE dough into 1-inch balls and place on prepared baking sheets. (Dough is easier to work with when well chilled.) Flatten dough with bottom of glass dipped in sugar.
BAKE for 11 to 12 minutes or until edges are firm to the touch. Cool on baking sheets for 5 minutes. Remove to wire racks to cool completely.
PLACE 2 to 4 cookies flat side up on microwave-safe plate. Place 4 to 5 chunks on each cookie. Place 1 marshmallow on its side on top of chocolate. Microwave on HIGH (100%) power for 10 to 15 seconds or until marshmallows are puffed. Immediately top marshmallows with flat side of other cookies and press together to make sandwiches. Cookies are best when eaten slightly warm!
NOTE: Cookies prior to assembling can be prepared up to 1 day ahead and stored in airtight container at room temperature. Or, cookies can be assembled, stored as stated and reheated in the microwave for 5 to 10 seconds.