Preheat oven to 325 degrees. Whisk flour, ground ginger, salt, baking soda, cinnamon, and cloves in a bowl.
With an electric mixer on medium speed, beat butter and sugar until pale and fluffy, 2 to 3 minutes. Mix in egg, then add molasses and candied ginger. Reduce speed. Gradually mix in flour mixture. Wrap dough in plastic, and refrigerate until slightly firm, 15 minutes.
Using a 1 1/2-inch ice cream scoop, drop balls of dough onto parchment-lined baking sheets. Roll each one in sugar, and return to sheets, spacing 2 inches apart. Using the bottom of a glass dipped in sugar, press dough to flatten into 3-inch rounds. Bake until edges are golden brown, 8 to 10 minutes. Let cool completely. Cookies can be stored in airtight containers up to 2 days.
Sandwich one scoop of sorbet with 2 cookies. Repeat, alternating sorbet flavors. Serve immediately, or freeze in airtight containers up to 3 hours.