How to Make It
In a pot of simmering salted water, cook the potatoes and turnips until tender, 15 minutes; drain. Transfer to a bowl and mash. Add the cabbage, brussels sprouts and leeks to the pot and simmer until tender. Drain and chop. Add to the potato mixture with the Worcestershire sauce and celery seeds and toss. Season with salt and pepper.
In a nonstick skillet, brown half of the vegetable mash in 2 tablespoons of the oil over high heat, stirring, 10 minutes; transfer to a baking sheet. Repeat with the remaining vegetables and 2 tablespoons of oil.
In the same skillet, melt the butter. Add the mushrooms and season with salt and pepper. Cover and cook over moderately low heat until tender, 8 minutes.
Form the mash into 16 patties and flour them; fry in the skillet in 1/4 inch of oil over moderately high heat, turning once, until browned, 6 minutes. Transfer to plates.
Wipe out the skillet. Heat a thin layer of oil, crack in the eggs and cook until over-easy. Top the patties with the eggs, garnish with the mushrooms and serve.