Combine eggs, celery, mayonnaise, salt and pepper, to taste and mix well. Using a crinkle cutter (if you have one) or a knife, cut carrots into 2 x 1/4-inch "fries" , set aside. Place a small piece of lettuce on each bun bottom and then top with egg salad, dividing it equally between the 8 buns. Top egg salad with a slice of cheddar cheese, tomato and pickle. Top with remaining bun half to form a burger. Serve with carrot "fries" and small bowls of ketchup and relish, if desired.