Put the potatoes in a large saucepan and cover with cold salted water. Bring to the boil, then simmer for 15 mins until they are tender but still hold their shape, and you can insert a cutlery knife easily.
Drain the potatoes and allow to steam-dry. Heat the oil with 1 tbsp of the butter in a large frying pan over a medium-high heat. Once the butter is foaming, add the potatoes, cut-side down, and fry undisturbed for 5 mins until golden.
Add the remaining butter along with the spinach, capers, lemon zest and juice. Stir everything together for a few mins so that the potatoes are coated and the spinach has wilted, then season to taste with salt and black pepper.