How to Make It
Peel limes with a vegetable peeler, avoiding white pith; place rind and sugar in the bowl of a food processor. Pulse until rind is roughly broken up and mixed with sugar. Transfer to a zip-top plastic bag; add 1/4 cup water, and seal, pressing out any air. Let stand at room temperature 24 hours, massaging as often as you can. Strain through a fine sieve, pressing on solids; discard solids.
Place watermelon, in batches, in a food processor; process until pureed, and pour into a strainer set over a large bowl. Strain, discarding solids. Reserve 14 cups juice. (Save any extra juice for another use.) Place 3 cups watermelon juice in a large ice mold or freezer-safe bowl or in 1-inch ice-cube trays; freeze until solid, about 8 hours.
Mix strawberry puree, vinegar, remaining 11 cups watermelon juice, rind mixture, gin (if desired), and tarragon in a large pitcher. Refrigerate punch 2 hours or overnight.
Break frozen watermelon juice into rough 1-inch cubes. To serve, add sparkling water to punch. Serve immediately in ice-filled glasses with a frozen watermelon cube.
Monello and Constantine restaurants, Minneapolis, MN