To assemble the salad, first bring a pot of cold, salted water to a boil. Gently add the eggs, turn down the heat and let simmer for 8 minutes. Place them into an ice bath to cool.
Core the tomatoes and slice into wedges. Fan the tomatoes onto each plate and drizzle with a bit of the vinaigrette.
Cut the potatoes in half and peel the eggs; set both aside.
Before you start cooking, have your entire mise en place ready. Heat a large fry pan over medium-high heat. Season the top of the salmon with a bit of salt and pepper. Once the pan is hot, add the olive oil, followed by the salmon, presentation-side down. Season the other side. Turn the heat down to medium and let it cook for about 2 minutes, without touching it. Once it has a nice golden crust, flip it over and continue to cook for another 1-2 minutes.
Test the salmon for doneness and remove just before it's done to your liking. Drizzle with a bit of the vinaigrette. Drain most of the oil from the pan, turn up the heat to medium-high, and cook the potatoes, cut side down. Once the potatoes are warmed through and lightly golden, turn them over. Add the beans and cook briefly. Season with salt and pepper to taste, and then add the shallots, garlic, olives, and the rest of the vinaigrette. Turn off the heat and gently toss to coat.
Add the basil and the warm vegetables to the greens and fold everything together. Cut the eggs in half and portion out the salad between the four plates. Add a piece of salmon and half an egg to each plate. Lastly, garnish with some of the chives et voila c’est toute. Bon appétit!