Soak the porcini in 1/4 litre of lukewarm water for 20 minutes. Take out of the soaking water, wash thoroughly and chop. Carefully transfer the soaking liquid to a pan, keeping back any residues. Add the chopped porcini and boil until all the liquid has evaporated. Leave to cool.
Break up the bread and pour the milk over it. Wipe the button mushrooms with a cloth and carefully twist out the stalks, being careful not to damage the caps. Preheat the oven to 200°. Finely chop half of the mushroom stalks. Chop the pancetta and the rinsed and dried anchovy fillets very finely. Wash and dry the basil leaves and chop finely.
Wash and dry the parsley, strip the leaves from the stalks and chop finely. Peel and press the garlic. Squeeze out the soaked bread and mix with the basil, parsley, garlic, porcini, pancetta, anchovies and chopped mushroom stalks.
Add the egg, season with salt, pepper and marjoram and mix well. Stuff the mushroom caps with the mixture. Grease a baking dish with 2 tbsp olive oil.
Place the mushrooms in the dish, stuffing side up, and sprinkle with breadcrumbs and the rest of the oil. Bake the stuffed mushrooms in the preheated oven (second shelf from the top) for about 30 minutes, until a crust forms on the stuffing. Cool slightly before serving.