Add all dressing ingredients into a blender except the oil and mix until combined. With the blender running, add the oil. Blend until well mixed, use added water if needed.
In a large salad bowl, toss in arugula, all the melon, and avocado. Toss with dressing.
Plate salads and top with slivered almonds and a drizzle of balsamic vinegar or cream.
Notes
Walnut oil is my personal preference for taste, but either oil works well in this salad.