Cook the potatoes in salted water until just tender, about 6 minutes. Add the green beans and cook until crisp-tender, about 3 minutes. Drain and rinse to cool. Cut the potatoes in half.
Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high. Add the salmon, skin-side down, and cook 3 to 4 minutes. Turn the fillets and cook until they are no longer translucent but still moist in center, 3 to 4 minutes more. Remove from skillet.
Whisk together the lemon juice, parsley, mustard, salt, pepper, and the remaining oil in a small bowl.
Divide the salmon, potatoes, green beans, tomatoes, and olives evenly among the plates. Drizzle the dressing over each serving. Serve warm or at room temperature.