Make the Juice:
Blend the honeydew, basil, and honey until smooth. Strain through a fine mesh sieve, pressing to extract all the juice.

Build the Cocktail:
Add the juice to a shaker with mezcal, lime juice, and a pinch of salt. Fill with ice and shake until cold and frothy, 10-15 seconds.

Serve:
Strain into a rocks glass over fresh ice. Garnish with a basil leaf or rim the glass with chili salt.