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Bring a pan of water to the boil, add the sea vegetables and blanch for about 30 secs, then drain.
Melt half the butter in a frying pan, add the mushrooms and season. Fry for 8-10 mins or until golden-crusted and reduced in size. Meanwhile, heat the rapeseed oil in a frying pan and fry the eggs gently for a couple of mins. Toast the sourdough until golden. Transfer the sourdough to plates and keep warm.
Add the rest of the butter to the mushroom pan along with the garlic, cook for a further 1 min, then toss in the sea veg to warm through briefly. Season and add the lemon juice.
Top the sourdough with the eggs and scatter over the sea veg and mushrooms. Spoon over any butter from the pan and grind some seasoning over the yolks. Serve while hot.