Preheat the oven to 220C/200C fan/Gas 7. Cut the potatoes into thick chips - leave the skins on for extra crunch and nutrients.
Toss the chips with 1 tablespoon of vegetable oil and a pinch of salt. Spread them out on a baking tray in a single layer - do not overcrowd them.
Bake for 25 minutes, turning halfway through, until golden and crispy.
When the chips are nearly done, heat the butter and remaining oil in a frying pan over medium-high heat.
Crack the eggs into the pan and fry for 2-3 minutes until the whites are set and the yolks are still runny.
Serve the chips piled on plates with the fried eggs on top. Season with salt and vinegar.