Heat oven to 350°F. Combine butter, brown sugar and sugar in bowl. Beat at medium speed, scraping bowl often, until creamy. Add honey, vanilla and egg; continue beating until well mixed. Add flour, graham crackers, baking soda and salt; beat at low speed until well mixed.
Drop 20 portions dough, 2 inches apart, onto ungreased cookie sheets. Bake 9-11 minutes or until edges are golden brown. Cool completely.
Line 1 cookie sheet with parchment or waxed paper. Place all cookies bottom-side up on cookie sheet. Spread about 1 tablespoon marshmallow crème onto 10 cookies. Spread about 1 teaspoon ice cream topping onto remaining 10 cookies. Refrigerate until ready to assemble sandwiches.
Chill baking sheet 5 minutes in freezer.
Scoop 10 (about 1/4 cup) ice cream portions onto chilled baking sheet. Return to freezer; freeze until ready to assemble sandwiches.
Thaw ice cream portions 4-5 minutes at room temperature. Place 1 portion onto marshmallow crème-topped cookie; top with chocolate-topped cookie, chocolate-side down. Press cookies together gently. Smooth ice cream with knife, if necessary.
Press mini chocolate chips into ice cream around edges of cookies, if desired. Place onto baking sheet; freeze immediately at least 2 hours or until set.
Wrap each frozen ice cream sandwich in plastic food wrap; place into large resealable freezer bag. Store frozen.