In a blender or food processor, blend chunks of watermelon until smooth and strain, using cheesecloth or fine-mesh sieve, into a container. Season with a pinch of salt.
In a shaker add 3 oz Vermouth bianco, .75 oz watermelon juice, .75 oz fresh-squeezed lemon juice, and finally ice. Shake vigorously for ~20-30 seconds until very cold and frothy. Strain into tall glass (or wine glass) with ice cubes and top with 3 oz of sparkling beverage of choice (tonic water for sweetness, sparkling water for refreshing, or sparkling wine for a bit more punch).
Enjoy with a sidecar of Pearl Street Caviar.