Preheat the oven to 180°C, 350°F, gas mark 4. Lightly butter 4 small casserole or ramekin dishes.
Melt half the remaining butter in a small saucepan, add the shallots and cook until soft but not coloured. Add the rest of the butter and the mushrooms and cook until soft. Add the parsley and season to taste with salt and pepper. Divide this mixture between the four dishes, make a dip in the centre of each dish and break an egg into each
Spoon 1 tablespoon of cream onto each egg and season. Stand the dishes in a roasting pan, half filled with hot water and bake in the preheated oven for 10-12 minutes until the whites and yolks are set.
If serving vulnerable groups, elderly people, toddlers, pregnant women and people who are unwell, cook eggs until the whites and yolks are solid.