Preheat oven to 200°C. Boil potatoes in a large pot of water for 8–12 minutes until just tender and easily pierced. Drain, shake to rough up, and steam dry briefly. Toss with olive oil, butter and salt. Transfer to a lined tray and roast for 30–35 minutes until golden and crispy, turning halfway.
Meanwhile, blitz capers, cornichons and liquid, dill, parsley, mustard, Kewpie and lemon juice in a small processor until smooth. Season to taste.