Bring a pot of water to a boil. Gently submerge eggs using a slotted spoon. Cook exactly 6 minutes for runny yolks and cooked whites (or longer, as desired). Transfer cooked eggs to ice bath and cool 2-3 minutes.
Prepare salad by spreading lettuce across a serving platter. Top with piles of onion, tomatoes, cucumber, avocado and radish. Drape slices of salmon overtop.
Peel eggs and add to salad. Slice eggs in half, length-wise directly over salad so that none of the runny yolks are lost.
Drizzle salad with EVOO and lemon juice and season with Everything-but-the-Bagel seasoning. Garnish with capers.