Preheat oven to 350°F.
On a large baking sheet toss bread cubes with 2 tablespoons oil and sprinkle with salt. Bake, stirring occasionally, until toasted and crisp, about 15 minutes.
In a blender combine melon, the flesh of 1 avocado, cucumber, basil, lime juice, garlic, salt, pepper, and remaining 2 tablespoons oil. Blend until completely smooth.
Pour soup into bowls. Dice remaining avocado and use to garnish soup along with croutons and a drizzle of olive oil.