When potatoes have cooled enough to handle but are still warm, quarter potatoes or chop potatoes into bite-sized pieces.
Add potatoes and 1 tablespoon of prepared dressing to large mixing bowl. Toss potatoes in dressing until fully coated, then set bowl aside and let potatoes cool completely.
Drain cooled green beans well and gently pat green beans dry with paper towels as needed. Add green beans to bowl with potatoes.
Rinse 4 heads Little Gem lettuce under running water, then drain lettuce and pat dry with paper towels if needed. Quarter or chop each head of lettuce, then place lettuce in bowl with potatoes and green beans.
Add desired amount of Nicoise olives, capers, anchovies, picklesand/or marinated artichoke hearts to bowl with lettuce and potatoes, then add 50% to 75% of remaining dressing. Toss all ingredients until well incorporated and coated in dressing.
Divide lettuce mixture evenly between serving bowls.
Drain water and ice from bowl of boiled eggs, then shake and toss bowl vigorously until egg shells have cracked enough that no large pieces of shell remain intact. Gently peel away egg shells and discard. Note: if needed, peel eggs under running water, using force of water to help dislodge any small shell pieces.
Once peeled, cut boiled eggs in half vertically. Add egg halves and 3 medium tomatoes (quartered) to serving bowls with lettuce mixture.
Use fork to flake tuna from 2 5-ounce cans chunk light tuna in oil, dividing tuna evenly between serving bowls.
Top salads with remaining salad dressing and season with sea salt to taste. Serve immediately.