Place the potatoes in a 3-quart / 2.8 L saucepan, cover with cold water, and add a generous pinch of salt. Bring to a boil and cook for 12 to 15 minutes, until a knife slides in easily.

Meanwhile, bring a 2-quart / 1.9 L saucepan of water to a boil. Lower in the eggs and cook for exactly 7 minutes for a jammy yolk that still holds together.

Drain the eggs and drop them into an ice bath for 5 minutes. Peel and halve them once cool.

Drain the potatoes in a colander and let them steam-dry for 2 to 3 minutes. Cut any larger pieces in half.

Whisk the mayonnaise, Greek yogurt, Dijon mustard, lemon juice, lemon zest, olive oil, salt, and pepper together in a mixing bowl until smooth.

Add the still-warm potatoes to the bowl and toss with two-thirds of the dressing so they absorb the flavor.

Fold in the celery, red onion, capers, and chopped dill, mixing gently so the potatoes don't break apart.

Check the flaked smoked trout for any missed pin bones, then fold it into the salad, or set it aside to layer on top.

Divide the arugula between bowls, spoon the potato salad over the top, and add the egg halves and trout.

Drizzle with the remaining dressing and scatter extra dill over each bowl before serving.