Preheat the oven to 170°C Gas mark 3. Put the wine, thyme and bay leaf in a small saucepan and reduce by half over a low heat. Add the shallot and veal or chicken stock and reduce until thick enough to generously coat the back of a spoon. Discard the thyme and bay leaf and set aside the shallot and wine.
Cut the chicken livers into small pieces. Heat the oil in a small frying pan and quickly sear the livers for 30 seconds. Season, put into a bowl and set aside.
Brush the sides of 4 cocottes or ramekins, about 8cm in diameter and 4cm deep, with the softened butter and season to taste, and divide between the cocottes. Carefully tip the egg into each one and bake the eggs until cooked to your liking.
Put a cocotte on each plate and serve immediately, with small slices of toasted country bread.