Season eggplant liberally with salt and let sit for 20 minutes to remove some of the bitter taste.
Preheat the oven to 400 degrees F. Brush eggplant and potatoes with olive oil and season with salt. Place on a foil lined cookie sheet.
Drizzle beets with olive oil and salt and place on a separate foil lined cookie sheet. Roast vegetables until tender, about 25 minutes, and set aside.
Meanwhile, hard boil your eggs. Put them in cold water, bring to a boil and simmer for 12 minutes. Let cool in an ice bath, peel and separate yolks from whites and dice.
To make dressing, process all ingredients in a food processor. Add in enough water to get desired texture and season with salt and pepper to taste.
To build salad, lay down a bed of arugula. Place in piles or rows the eggplant, potatoes, beets, cucumbers, tomatoes, egg white and yolks. Drizzle with dressing and garnish with chives.