Put the porcini in a small bowl, then heat the milk, pour it over the porcini mushrooms and leave them to soak for 30 minutes.
Then heat the butter in a medium frying pan over a gentle heat, stir in the shallots and let them cook gently for 5 minutes. Next, strain the porcini into a sieve lined with kitchen paper, reserving the soaking liquid, and squeeze the porcini dry.
Chop them finely and add them to the pan, along with the fresh mushrooms and the balsamic vinegar. Season with salt, pepper and nutmeg. Give it a good stir, then cook gently, uncovered, for 30-40 minutes, until all the liquid has evaporated.
About 15 minutes before the mushrooms are ready, put the pasta on to cook. Then, 2 minutes before the pasta is cooked, mix the crème fraîche into the mushrooms with the soaking liquid, and warm through.
Drain the pasta in a colander, return it to the hot pan and quickly mix in the mushroom mixture, then place the pasta back on a gentle heat so it continues to cook for 1 more minute while it absorbs the sauce.
Take it to the table in a hot serving bowl and hand the Parmesan round separately.