Bring 1 in. water to a boil in a large saucepan. Set potatoes in a steamer basket and steam in pan, covered, until tender, about 20 minutes. Cool in ice water, then pat dry. Cut potatoes into chunks and put in a large bowl.
Meanwhile, bring some water to a boil in a saucepan. Add peas; cook until tender, 3 minutes. Drain and transfer to ice water, then drain again.
Whisk together vinegar, mayonnaise, and salt in a small bowl to combine. Add onions, peas, and half the dressing to potatoes and gently stir to coat. Add eggs and 3 tbsp. tarragon and gently stir to coat.
Spread remaining dressing on bottom of a wide bowl, add salad, and sprinkle with more tarragon if you like.
*Look for spring onions (regular onions picked young) at farmers' markets in spring and at Latino markets year-round. They have a fatter bulb than green onions--which have less crunch but make a good substitute. For perfect hard-cooked eggs, cover them in cold water in a small saucepan and bring to a boil. Remove from heat and let stand 12 minutes. Plunge cooked eggs into ice water, crack all over, and let sit in the water for a few minutes before peeling.