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 a third of the olive oil and all the butter in a large frying pan over a medium heat and fry the leeks 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 a third of the olive 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 a third of the olive 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.