In a medium bowl, cover the sliced onion with cold water and soak to mellow the flavor, about 15 minutes; drain.
Meanwhile, place the potatoes in a medium pot; add enough water to cover by 1 inch. Salt the water, add 2 tbsp. vinegar and bring to a boil over medium-high. Reduce the heat to medium and cook until tender, about 10 minutes. Drain; rinse under cold water until cool.
In a large bowl, whisk the remaining 2 tbsp. vinegar, 2 tbsp. oil and the mustard; season with salt and pepper. Add the cucumber, parsley, onion and potatoes; toss to coat. Divide among plates.
In a large nonstick skillet, heat the remaining 1 tbsp. oil over medium-high. Pat the salmon dry with paper towels, season and cook without moving until golden, 4 minutes. Flip and cook until salmon flakes easily with a fork, about 4 minutes more. Serve on top of the salad.