For the bubble and squeak cakes, place the carrot, parsnip, potato, celeriac, cabbage and kale in a large pan of salted boiling water, and cook until very soft, about 20-25 minutes. Drain, and return to the pan.
Roughly mash the vegetables together.
Heat half the butter in a frying pan and soften the leek for 4-5 minutes. Mix into the mashed vegetables and season, to taste, with salt and freshly ground black pepper.
Divide the mixture into 4, and shape into patties with your hands. Refrigerate for 30-45 minutes while you make the gravy.
For the gravy, heat the oil in a frying pan over a medium heat and fry the onion for 6-8 minutes, or until softened and caramelised.
Stir in the flour, and cook for a minute.
Pour in the red wine and add the thyme. Stir well over a high heat until boiling, then lower the heat and continue to simmer for 2-3 minutes to reduce.
Add the stock and balsamic vinegar, and continue to simmer over a low heat while you fry the bubble and squeak cakes.
Remove the bubble and squeak cakes from the fridge. Melt the remaining butter in a frying pan and gently fry the cakes until golden-brown and crisp on both sides, about 3-4 minutes per side.
Meanwhile, check the gravy, and season, to taste, with salt and freshly ground black pepper.
Melt the remaining butter in another frying pan and fry the eggs for 2-3 minutes, then season, to taste, with salt and freshly ground black pepper.
To serve, place 2 bubble and squeak patties on 2 serving plates and top each with an egg. Drizzle the gravy round the edge to garnish.
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