1. Peel and chop the shallots.
2. Melt the butter in a frying pan. Add the shallots, then the flour. When they start to brown, moisten with the wine and stock. Season with salt and pepper and simmer for 20 minutes.
3. Shortly before the sauce is finished, bring 2 litres (approx 3 1/2 pints) of water and the vinegar to the boil. To poach the eggs, break them over the surface of the water. Reduce the heat and simmer for 4 minutes. Remove the eggs with a skimmer and place on a serving dish.
4. Add mustard to the sauce and mix well. Remove from the heat and pour over the eggs. Serve at once.