Peel potatoes and cut into 1-inch pieces. Put in a saucepan and cover with water. Bring to a boil; cover, reduce heat to medium-low, and cook for 12 to 18 minutes, until potatoes are fork tender but still firm. Drain and let cool with cover ajar.
Combine the cooled potatoes with the chopped hard cooked eggs, onion, and celery. Gently stir in 1/2 cup mayonnaise and the mustard, along with the pepper. Add more mayonnaise, as needed. Add salt to taste.
Calories per serving: 405