Cut all the melons in half. Scoop out the seeds and pulp of the Golden Kiss Melon (cantaloupe) and the Honeydew, and place them on a strainer with a bowl underneath to catch all the juice. Press the pulp and seeds with a spoon or spatula to extract as much juice as possible. Discard the seeds and pulp and set aside the juice.
Use half of each melon to make melon balls using a melon baller and cut in cubes using a knife. Reserve the other half of each melon for the drink.
Make a few melon balls and cubes from each melon and set them aside in the fridge. Scrape the remaining flesh from the cantaloupe and honeydew and place it in the blender.
Remove the flesh from the reserved cantaloupe and honeydew and add it to the blender along with 12 mint leaves. Use the smoothie program or blend until smooth. Transfer the mixture to a pitcher or any container and place it in the fridge. Repeat the same process with the watermelon.
There are two ways to serve, whichever is easier for you.
Divide the melons balls and cubes into two bowls. Pour the cantaloupe and honeydew juice into one bowl and the watermelon juice in the other bowl, then garnish with mint leaves.
Alternatively, serve in a glass or a small dessert bowl. Pour the cantaloupe/honeydew juice and add some melon balls and cubes, garnishing with mint leaves. Do the same with the watermelon.
Notes
I suggest using the Golden Kiss Melon and the Golden Honeydew as they blend so well together and are very tasty.
If you don't have a melon baller, use a knife to cut instead.
You can add 1 teaspoon to 1 tablespoon of lime juice to the blended drink. You can also top it with crumbled feta cheese. These are optional. The drink is delicious with just melon and mint.
Make this ahead of time so juices meld together. It is best chilled before serving. If serving for dinner, prepare it at lunchtime and place it in the fridge.
You can rim the glass with sugar or salt, if desired, though it's not necessary due to the drink's sweetness. If you'd like to rim the glass, wet the edge of the glass with a cube of watermelon and dip it in sugar or salt.
Leftover is good for up to 2 days in a covered container in the fridge.