Hard-boil the eggs. Place the eggs in a saucepan and cover them with water. Bring the water to a boil, then reduce the heat to low. Simmer for 12 minutes. Transfer the eggs to an ice bath to cool.

Peel the eggs. Once the eggs have cooked, peel them, discard the shells, and chop them into small pieces.

Put it all together. In a large bowl, combine the eggs, onion, celery, pickles, bell peppers, shredded cheddar cheese, mayonnaise, and Dijon mustard. Mix gently until everything is well coated in the dressing.

Season. Taste the egg salad and season with salt and pepper to taste.

Chill and serve. Refrigerate the egg salad for at least 30 minutes and serve cold on its own, in a sandwich, or with your favorite crackers.