Bring a large pan of lightly salted water to a boil. Add the potatoes, bring back to a boil, and simmer over medium heat for 8-10 minutes or until tender. Remove the potatoes from the pan using a slotted spoon and set aside to cool slightly.
Once the potatoes are cool enough to handle cut them into wedges with a sharp knife.
Pit the mixed olives with a cherry pitter or small sharp knife and cut them in half.
Using a sharp knife cut the anchovy fillets into thinner stripes
Heat the olive oil in a large, heavy skillet. Add the potato wedges and rosemary. Cook over medium heat, stirring occasionally, for 7-8 minutes or until the potatoes are golden.
Stir in the olives and anchovies and cook for 1 minute or until completely warmed through. Transfer the potato mixture to warmed serving plates and serve.