Start by making the dressing. To do so, place all dressing ingredients in a jar, put the lid on, and give it a vigorous shake. Set it aside.
To cook the potatoes: Place them in a medium-sized pot and add in water just enough to cover them by an inch. Stir in 1 tablespoon kosher salt. Bring it to a boil over medium-high heat. Then turn down the heat to medium-low and cook until a knife inserted into a potato comes in and out easily 20-25 minutes. Remove the potatoes from the pot with a slotted spoon and place them in a bowl. Do not discard the water just yet. We will cook the green beans in it.
To par-cook the green beans, place them in the hot potato water and cook for 3 minutes until they are softened but still crunchy. Drain and set them aside.
Cook the eggs while potatoes are cooking. ** To do so, bring 1-inch water to a boil in a small saucepan over high heat. When it comes to a boil, add in the eggs (right out of the fridge is fine). Put the lid on and cook for exactly 7 minutes. Meanwhile, prepare an ice bath by filling up a bowl with cold water and ice. After 7 minutes are completed remove eggs from the pot and place them into the ice bath to stop cooking. When they are cool enough to handle (5-7 minutes later), peel them and set aside.
To roast the salmon: Preheat the oven to 300 F degrees. Line a baking sheet with parchment paper and set aside. Using a sheet of paper towel, pat-dry the salmon fillets. Brush them lightly with olive oil and season with salt and pepper on each side. Place fillets onto the baking sheet skin side down. Arrange two slices of lemon underneath each salmon fillet (as shown in the photos.) Bake for 13-15 minutes in the oven or until it registers 125 degrees when the thickest part of the fish is inserted with an instant thermometer.
To assemble the salad: Drizzle half of the dressing over the potatoes while they are still hot so that they can absorb some of it. Add in reserved green beans, cucumber, tomatoes, olives, sliced avocados, and capers into the bowl.
Using two forks, gently break apart the now-cooked salmon into smaller (bite-sized) pieces. Place it on top of the salad.
Slice the eggs and add them to the bowl.
Drizzle the salad with the rest of the salad dressing. Garnish with parsley and serve.