Place halved fingerling potatoes in a medium pot. Cover with water. Bring potatoes to a boil over medium-high heat. Reduce heat to medium and let potatoes simmer until tender, about 10-15 minutes. Remove potatoes from hot water and place in a large bowl, reserving hot water in pot.
In same pot, bring water back to a boil. Once boiling add green beans and let simmer 5-8 minutes until tender. Drain beans and immediately plunge them in ice water to cool them immediately. Drain beans and combine with potatoes.
Sprinkle salmon fillets on both sides with salt and pepper. In a large nonstick skillet over medium-high, heat olive oil until shimmery. Place salmon fillets in hot pan and sear on first side 3-4 minutes or until golden. Carefully flip fillets and cook on opposite side 5-6 additional minutes or until salmon is a light pink. Set aside.
Toss eggs, tomatoes, and lettuce with cooked beans and potatoes in a large bowl. Set aside for a moment while you prepare the dressing.
Make the dressing: In a jar with a tight-fitting lid, shake all dressing ingredients until smooth. Season with salt and pepper to taste.
Drizzle dressing over salad and gently toss to coat. Arrange seared salmon on top and drizzle with more dressing. Serve salad immediately once tossed in dressing. Enjoy!