Make the dressing: Combine all the ingredients for the dressing in a blender or food processor. Season with ¼ teaspoon salt and 1/8 teaspoon pepper. Puree until smooth and emulsified. Taste and adjust for seasoning with salt and pepper (see note). Set aside.
Make the salad: In a medium bowl, combine cucumber, avocado and half the green onions. Drizzle with enough dressing to coat. Toss gently to combine.
To serve: Arrange the cucumber and avocado mixture in a serving bowl or platter. Scatter the remaining green onions, radishes, red onions and cheese on top. Drizzle with desired amount of dressing and season to taste with salt and pepper. Serve immediately and enjoy!
Start with 3 tablespoons of oil in the dressing. Add more, one teaspoon at a time, until desired consistency is achieved. For a richer, thinner dressing, use the full 4 tablespoons of oil.
If you want to make this salad a couple hours in advance, prepare the recipe as instructed, however do not add any salt! Salt will cause the cucumbers to seep water and the salad will become watery. Cover the salad tightly with plastic wrap, and gently press the plastic to adhere to the top of the salad to keep the oxygen out. Exposure to oxygen will cause the avocados to turn brown.
Dressing can be made in advance and stored in an air tight container in the refrigerator for up to 3-4 days.