Tip the potatoes into a large pan of cold salted water, then bring to the boil and cook for 6-8 mins until just tender. Drain well and leave to steam-dry for 10 mins.

Meanwhile, heat half the oil and all the butter in a large frying pan over a medium heat and fry the leeks, kale stalks and sage sprig for 10-12 mins until softened to the point of falling apart. Stir in the garlic and cook for 3 mins more before mixing in the kale leaves. Cook for another 5 mins until the leaves have reduced in volume and turned dark green. Scrape the mixture into a bowl and set aside.

Heat the remaining oil in the frying pan over a high heat and tip in the boiled potatoes, stirring to coat in the oil. Fry for 15-20 mins until golden and crispy. Return the leek mixture to the pan and stir to combine. Season to taste and divide the hash between plates.

Meanwhile, cook the eggs. Heat the oil in a separate pan over a medium-high heat and fry the sage leaves for 1-2 mins until darkened and crispy. Remove to a plate lined with a sheet of kitchen paper to drain. Return the pan to the heat and crack in the eggs. Fry, basting occasionally in the sage oil, until crispy at the edges, about 2-3 mins. Top each plate of hash with a crispy fried egg, and scatter over the fried sage leaves. Garnish with a little grated cheese, if you like, and season with black pepper to serve.