Peel and cut the potatoes into medium cubes. Boil them in salted water until tender but not falling apart. Drain and place them in the bottom of a salad bowl.

Finely chop the green onions and celery, then add them to the potatoes. Gently toss to combine.

In a jar with a tight-fitting lid, shake together the olive oil, vinegar, sugar, horseradish, salt, pepper, lemon juice, and lemon zest until the mixture thickens into a creamy dressing.

Tear the smoked salmon into pieces by hand and mix it with the potatoes.

Pour the dressing over the salad, toss once more to combine the flavors, garnish with chopped dill, and serve the salad warm.