Preheat the oven to 190C/375F. Cut a slit in the side of each piece of monkfish to create a pocket. Open each pocket out a little and arrange the peppers and basil inside, then season with a pinch of salt and plenty of pepper. Close over sandwiching in the pepper mixture. Lay two Parma ham slices out on the work surface, slightly overlapping, then place one monkfish fillet on top and wrap in the Parma ham to enclose the monkfish completely. Repeat with the remaining fillets.
Heat a tablespoon of the olive oil in a large ovenproof frying pan and sear the monkfish pieces all over for 3-4 minutes until the Parma is crisp and golden. Transfer to the oven and roast for another 10-12 minutes until firm to the touch and just cooked through.
Meanwhile, place the potatoes in a pan of cold water over a high heat and add a pinch of salt. Bring to the boil and cook for 5 minutes until partially cooked. Drain and set aside.
Heat the remaining oil with the butter in a large non-stick frying pan over a medium heat. Add the potatoes, then season with a pinch of salt and plenty of pepper and sauté for 8-10 minutes until lightly golden and tender, stirring occasionally.
Increase the heat to high, add the kale and sauté for another 2-3 minutes, until the kale is tender and just crisp around the edges. Arrange the Parma wrapped monkfish on warmed plates with the crispy new potatoes and kale alongside to serve.