Wash the potatoes thoroughly and cover them with water in a large saucepan, cook with the lid closed for about 20-25 minutes. Then drain, rinse briefly with cold water and peel while still warm. Let cool completely and then cut into thin slices.
Boil the eggs in gently simmering water for approx. 6 - 7 minutes until they are waxy. Halve the washed tomatoes, remove the pulp and cut into wedges. Halve or quarter the drained artichokes, depending on their size.
For the dressing, chop the peeled garlic very finely and mix well with the other dressing ingredients. Quite a lot of salt and pepper, as the salad swallows a lot of the seasoning.
Wash arugula and cut off the stems if necessary. Chop coarsely. Transfer to a large bowl. Add the potatoes, tomatoes and artichokes. Mix everything carefully with the dressing.
Peel the cooled eggs and cut into wedges or slices. Arrange decoratively on the salad with the torn anchovy fillets and some finely chopped parsley.