Preheat oven to 400°F/200°C/Gas Mark 6
Bring a small pot of water to a boil and add eggs. Boil for 6 - 10 minutes, depending on how set you like your yolks. Peel and set aside.
Line a half sheet pan with parchment paper and lightly oil paper with the olive oil.
Season potatoes with 1/4 tsp salt and 1/8 tsp black pepper. Place cut side down on sheet pan and bake for 8 minutes.
Carefully add salmon to hot sheet pan, buttered side down and bake for an additional 8 minutes.
Remove sheet pan from oven, flip salmon over and add tomatoes and green beans, coating them in a bit of the olive oil from the pan. Bake for an additional 4 - 6 minutes.
Divide chopped romaine lettuce evenly between 2 bowls.
Slice eggs in half and place 2 halves on each salad.
Top each salad with 1 piece of salmon, half of the potatoes, tomatoes, green beans and olives.
Drizzle with vinaigrette and serve.