Add potatoes to a large sauté pan and cover with 2 inches of cold water. Place pan over medium-high heat and bring to a boil; season with 2 teaspoons salt, reduce heat to medium and simmer until potatoes are fork-tender, about 20 minutes. Using a spider or slotted spoon,transfer potatoes to a large bowl; toss with a splash of oil and set aside.
Add green beans to simmering water, adding additional water as needed, and cook until crisp-tender, about 3 minutes. Meanwhile, fill a large bowl with ice water. Using a spider or slotted spoon, transfer green beans to ice water bath and set aside.
Reduce heat to low, and using a spider or slotted spoon, gently lower eggs into water. Bring water back up to a boil and cook eggs 7 minutes. Using a spider or slotted spoon transfer eggs to ice water bath; let cool completely.
Drain green beans and eggs; pat green beans dry.
Arrange lettuce leaves on a large platter. Arrange potatoes, green beans, cucumbers, and tomatoes over lettuce. Peel and halve eggs; arrange on platter, nestling into veggies.
Drizzle Dill Ranch Dressing over salad, sprinkle with fresh dill, chives, salt and pepper.