Boil the eggs: Place eggs in a large pot, cover with water, and bring to a boil over medium-high heat. Once boiling, cover with a lid, remove from heat, and let stand in hot water for 15 minutes. Then, transfer eggs to ice-cold water.
Boil the potatoes: Add cubed potatoes to a separate pot, cover with water, and bring to a boil. Cook for 15-20 minutes until tender but not overcooked. Drain and rinse under cold water.
Prepare the dressing: Halve the boiled eggs, remove yolks and place in a bowl. Mash yolks and mix with mayonnaise, mustards, relish, salt, and pepper until smooth.
Combine ingredients: Chop egg whites coarsely. In a large bowl, mix chopped egg whites, cooked potatoes, celery, red onion, and green onions. Fold in the dressing until well combined.
Chill and serve: Garnish with paprika, cover, and refrigerate before serving. Add halved hard-boiled eggs and fresh dill for garnish when serving.