Working in two batches, purée the honeydew, avocados, lime juice and salt until smooth. Pour through a single-mesh strainer into a container.

Refrigerate soup until chilled, at least 2 hours and up to 1 day.

Mix the cucumber, jalapeño, mint, lime juice, and red onion in a medium bowl. Sprinkle with salt to taste.

Holding the avocado half in one hand, make 1/4-inch crosshatch cuts through the flesh with a table knife, cutting down to but not through the skin.

Separate the diced flesh from the skin by gently scooping out the avocado cubes with a soup spoon.

Add avocado to the bowl with the salsa and mix gently. Season with additional salt to taste.

Cover and refrigerate salsa until ready to serve soup. To serve, ladle soup into bowl and garnish with a generous spoonful of salsa.