Cook the potatoes in a covered pan of boiling salted water for 15-20 minutes until tender.
Meanwhile, cook the kale. Heat a knob of butter and two tablespoons of water in a heavy-based pan with a lid. When the butter has melted and formed an emulsion, add the kale with a pinch of salt. Cover, shake well and cook over a high heat for 1 minute. Shake the pan again and cook for another minute. Drain off any liquid and then season the kale with pepper.
Drain the potatoes, add in the milk and mash until smooth, then beat in the kale and the remaining butter. Season to taste with salt and pepper.