Preheat oven to 425 F. Lightly grease a round 12-inch ovenproof baking dish or cast iron skillet which you have a lid. Transfer to the oven and heat for 5 minutes.
In a large bowl, combine the potatoes, red onion, kimchi, gochujang, miso paste, garlic, olive oil, and 1/4 tsp salt and toss thoroughly coated. Remove the pan from the oven, tip in the potato mixture, and spread out evenly. Bake for 20-25 minutes, uncovered, rotating the pan halfway through, until golden brown and crisp on top.
Making eight wells in the potato mixture with the back of a spoon. Crack an egg into each hole, then cover the pan with a lid or foil and return to the oven for another 8 minutes, until the whites are cooked.
For the sauce, in a small bowl combine the lime juice, gochujang, olive oil, scallions, and sesame seeds and stir to mix.
Drizzle the sauce over the eggs and serve straight from the pan, with the lime wedges to squeeze on top.