Place the udon noodles into a bowl and cover with hot water for 1–2 minutes to loosen. Drain well and set aside.
Heat the oil in a large frying pan or wok over medium-high heat. Add the garlic and the white parts of the spring onions and cook for about 30 seconds until fragrant.
Add the chopped kimchi and cook for 2–3 minutes, allowing it to caramelise slightly around the edges.
Stir in the gochujang, soy sauce, mirin, sesame oil, sugar (if using) and kimchi juice. Cook for another 30 seconds to bring everything together.
Add the drained udon noodles and butter. Toss for 1–2 minutes until the noodles are glossy, well coated and heated through.
Stir through the spring onion greens. Taste and adjust seasoning if needed.
Divide between bowls and finish with crispy shallots, toasted sesame seeds and a soft-boiled egg if using.