Whisk yogurt, mayonnaise, mustard, salt and pepper in a medium bowl. Discard one egg yolk. Chop the remaining eggs and transfer to the bowl. Add celery and onion and stir to combine. Cut lettuce leaves in half and double-layer them to make 2 lettuce wraps. Divide the egg salad among the wraps and top with basil. Serve with carrot sticks on the side.