Cut off stems of artichokes. Rub cut ends with lemon juice. Cut off the tips of the artichokes. Cook artichokes in salted water with the juice of ½ lemon until tender, 40-45 minutes. Remove leaves, remove the inner chokes and cut the bottoms into slices.
Heat 2 tablespoons olive oil in a pan. Add artichoke bottoms and sauté. In a large bowl, mix remaining olive oil with the remaining lemon juice. Season with salt and pepper. Add artichoke bottoms. Rinse anchovy fillets, pat dry and chop. Rinse tomatoes, cut into quarters and remove the seeds. Cut the tomatoes into slices. Chop the olives. Add anchovies, tomatoes and olives to the artichoke bottoms and allow to marinate briefly.
Rinse herbs thoroughly. Set some chive aside and cut remaining chives into rolls. Pluck chervil into small pieces. Arrange the salad on the chives and serve sprinkled with remaining herbs.