Cook potatoes in boiling water to cover and salted with 1 teaspoon salt 40 minutes or until tender; drain and cool 10 to 15 minutes.
Stir together mayonnaise, mustard, pepper, and remaining 1 1/2 teaspoons salt in a large bowl.
Peel potatoes, and cut into 1-inch cubes. Add warm potato cubes, grated eggs, celery, and onion to bowl, and gently toss with mayonnaise mixture. Serve immediately, or, if desired, cover and chill.
Note: To reduce cooking time, use 4 extra-large baking potatoes (about 1 pound each), peeled and cut into 1-inch cubes. Proceed as directed, reducing cooking time to 20 minutes or until tender. Drain and cool 10 minutes. Increase mayonnaise to 1 1/2 cups, and proceed as directed.