Preheat your oven to 350°F / 175°C. Spread the bread cubes onto a large, rimmed baking sheet. Spray the cubes lightly with avocado oil spray, if desired. Toast the cubes in the oven for 8-10 minutes, or until the edges of the bread cubes are golden. Remove the bread from the oven.
Cut both avocados in half and remove their pits. Add one half avocado, along with the olive oil, water, lemon juice or vinegar, shallot, basil, salt, and pepper into a blender and blend until smooth. Set this dressing aside.
To prepare the salad, combine the toasted bread cubes, cucumber, romaine, radishes, and white beans together in a very large mixing bowl. Cut the remaining one and a half avocados into cubes and add them to the bowl. Pour all of the dressing over these ingredients. Toss the salad well, taking care to mix all of the ingredients with the dressing. Serve right away.