Preheat oven to 375°. Line two baking sheets with parchment paper.
In a large bowl mix together crumbled cookie dough and molasses. Add flour, ginger, and cinnamon; mix together with hands.
Form dough into 1-inch balls (2 tsp.). Place balls on baking sheet 2 inches apart. Using a flat-bottom glass dipped in sugar, gently press each ball into a 1 1/2-inch round.
Bake for 6-8 minutes or until cookies are set and edges are slightly browning. Cool on baking sheet 3 minutes; remove to wire rack to cool completely.
To assemble sandwiches, place 2 Tbs. ice cream on 1 cookie pressing lightly to flatten. Top with another cookie. Roll edges in crushed peppermint candies, if desired. Repeat with remaining cookies. Wrap and freeze at least 8 hours.
Use raspberry sherbet in place of the peppermint ice cream.