To make the melon ice cubes, slice one honeydew melon in half and scoop out the seeds. Then slice into 6 wedges and run a knife very close to the rind to remove the fruit. Use a knife to cut the fruit into ice cube shapes (alternatively, use a melon baller to scoop out fruit).
Arrange fruit on a parchment-lined baking sheet and freeze for 1-2 hours, or until firm (like ice cubes).
In the meantime, remove seeds from the remaining half of the melon and scoop the fruit into a large jar (you should have ~2 cups of melon as recipe is written // adjust if altering batch size).
To the jar, add lime juice and organic cane sugar (or stevia) and use a muddler (or something with a flat edge) to smash and muddle together until it looks like a purée.
Set a fine mesh strainer over a mixing bowl and add the purée, then press to extract the juice. Continue pressing until all juice is extracted. Discard (or compost) remaining pulp, or reserve for smoothies. Set juice in refrigerator until melon cubes are frozen.
Once frozen, add melon cubes to desired number of serving glasses, filling 3/4 of the way up. Then top with the melon-lime juice, filling just less than halfway full.
At this time you can add extras such as fresh cherries, cucumber, mint, or alcohol of choice (see notes). Then top with club soda / sparkling water, stir gently, and enjoy!
Best when fresh. Store melon cubes in a freezer-safe container in the freezer up to 1 month. Juice will keep covered in the refrigerator for a few days, though best within the first 24 hours. Shake to refresh as it will separate.
*If subbing stevia for the cane sugar, add sparingly as it’s much sweeter than cane sugar! Start with less than 1/8th tsp and add to taste. *To make this drink boozy, add 1 ounce white rum (per drink) for tropical vibes, or 1 ounce gin (per drink) for drier flavor. Add alcohol after the juice and before the club soda. *Nutrition information is a rough estimate calculated with organic cane sugar and without add-ins (like cherries or alcohol).