Place eggs in a single layer in a saucepan. Cover with cold water by 1 inch. Bring to a full boil, then reduce to medium heat and cook for 10 minutes.

Transfer eggs immediately to a bowl of ice water. Let sit 5 minutes, then peel under cold running water and pat dry.

Coarsely chop 4 eggs into chunky irregular pieces. Mash the remaining 2 eggs with a fork until nearly smooth.

In a medium bowl, whisk together the mayonnaise, Dijon mustard, and lemon juice. Add salt, pepper, and paprika. Taste and adjust seasoning so the dressing is slightly bolder than you want the final result to be.

Add the chopped eggs, mashed eggs, celery, and green onion to the dressing. Fold gently until evenly coated, stopping as soon as everything is combined. Taste, adjust seasoning if needed, and serve immediately or refrigerate until ready.