Bring the water to a boil in a large pot over high heat. Add in the shrimp and boil until pink on the outside and opaque in the middle, about 3 minutes. Drain shrimp and run under cold water to quickly cool them. Spread shrimp out onto paper towels to drain well.
In the meantime, cut each hard boiled egg in half, remove the yolks, discard 2 yolk halves, and chop the remaining 2 yolk halves with all of the whites.
In a medium bowl, mix together the green onions and the next 10 ingredients. Gently toss in the shrimp and the eggs.
Place 1 cup of salad greens onto each of 4 plates, top with 3/4 cup of shrimp salad, and garnish with 2 lemon wedges.