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1
Melt half the butter in a deep frying pan and add the onion, carrot, celery and garlic, sauteing for 5 minutes until the vegetables start to colour. Add all other sauce ingredients (except the flour and residual butter) and bring to a boil. Lower the heat and leave on a gentle simmer for 40 minutes. Strain through a fine sieve into another pan, pressing the vegetables to extract all the flavour.
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2
While the sauce is simmering, heat half the butter for the garnish in a small pan over a medium-high flame. Add the shallots and sugar, cooking until golden. Add the stock, pop on a lid and simmer for 10 minutes, until tender. Lift off the lid and turn up the heat slightly to reduce the liquid, leaving the shallots nicely glazed. Set aside and keep warm.
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3
In a separate pan fry the bacon on a medium heat with the remaining butter until lightly browned. Add the mushrooms and fry until tender. Season to taste with salt and pepper, then set aside and keep warm.
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4
When ready to serve, bring a large shallow pan of water (about 5cm/2 inches deep) to the boil. Reduce the boiling water to a simmer and add the vinegar and 1/2 tsp of salt. Give the water a quick stir then carefully break an egg into the centre of the swirling water. Leave to poach gently for 3 minute then lift out with a slotted spoon and drain on kitchen towels. Repeat with the remaining 3 eggs.
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5
At the same time, bring the sauce back to a simmer. Mix the remaining 1 tbsp butter and flour together with a spoon then add the mixture to the sauce. Simmer for 2-3 minutes to thicken and cook out the flour. In a frying pan, fry your slices of sourdough with a little olive oil for a couple of minutes each side (alternatively, you can just toast them).
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6
To serve, place a piece of sourdough on a plate and top with two eggs (or one if you're serving 4). Scatter over the shallots, mushrooms and bacon then spoon over 3-4 spoonfuls of sauce.
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7
Eat at once, preferably alongside a nice glass of red burgundy.
