Heat oven to 325°F.
In large bowl, beat butter and brown sugar with electric mixer on medium speed until light and fluffy. Add egg and vanilla; beat until blended. Add flour, cracker crumbs and salt; on low speed, beat about 1 minute or until stiff dough forms.
Shape dough by heaping teaspoonfuls into 60 balls. On ungreased cookie sheets, place balls 2 inches apart. With thumb, make indentation in center of each.
Bake 10 to 12 minutes or until cookies are firm and edges are just beginning to brown. Lightly press 2 marshmallows in center of each cookie; bake 2 to 3 minutes longer. Top marshmallows on each cookie with 1 rectangle of chocolate; let stand 2 to 3 minutes. With tip of knife, gently spread chocolate over marshmallows. Let stand until chocolate is set.