Put everything but the cookies in a food processor. Process until smooth.
Line a shallow 13-inch-by-9-inch metal pan with plastic wrap, leaving enough overhanging plastic to cover the filled pan. Scrape the fruit mixture into the pan, cover with plastic, and freeze until solid, at least 4 hours or overnight.
Break into small chunks with a sturdy metal spatula and transfer to a food processor. Pulse until soft and snowy but not melted, about 1 minute. Scoop into dessert cups and serve with the cookies.
Tip: For a smoother sorbet, add 1 tablespoon Malibu rum. Adding alcohol lowers the freezing point of water, which keeps the sorbet from becoming too crystalline and granular.