Heat the oven to 200C (180C fan)/390F/gas 6. Put a large, ovenproof saute pan for which you have a lid on a medium-high heat, and add the butter and oil. Once hot, add the leeks, a quarter-teaspoon of salt and plenty of pepper, and cook, stirring occasionally, until the leeks have softened and are just beginning to colour – about eight minutes. Add the chopped thyme and garlic, cook for two minutes more, until fragrant, then turn off the heat and leave to cool slightly, for 10-15 minutes. When the leeks have sat for 10 minutes, put the cream, milk and 200ml water in a small saucepan on a medium heat, bring to a gentle simmer, and keep warm on a low heat.
Stir the sauerkraut, chives, potatoes, half the cheese, three-quarters of a teaspoon of salt and a generous grind of pepper into the cooled leeks, and smooth out the top so the potatoes are lying flat. Pour over the warm cream mixture, then sprinkle on the rest of the cheese and top with the thyme sprigs. Cover the pan, bake for 50 minutes, then remove the lid and bake for 30 minutes more, or until golden and bubbling. Leave to rest for about 15 minutes before serving directly from the pan.