Drizzle 2 slices of ciabatta (or 2 split rolls) with olive oil and vinegar. Place the anchovies in a bowl and smash with a fork, then smear half of the mixture onto each slice.
Layer on the tomatoes, red onions, artichokes, olives, celery leaves, and the hardboiled eggs, if desired. Season with salt and pepper. Sandwich with the remaining slices and press down gently but firmly.
Wrap sandwiches tightly with plastic film or wax paper and set aside for at least 20 minutes before eating to let flavors mingle.