Cook potatoes in boiling salted water for 8-10 minutes or until tender. Cool.
Meanwhile, heat oil in a frypan over medium heat. Cook onion, garlic and chilli, stirring, for 5 minutes until softened. Add anchovies and cook, stirring, for 1-2 minutes until anchovies dissolve. Add tomatoes, olives and capers, then cook for 1-2 minutes until warmed through.
When cool enough to handle, peel the potatoes and chop into 3cm pieces. Place potatoes in a bowl with the onion mixture and parsley, then toss well to combine. Top with parmesan and serve.