Place the potatoes in a pot, cover with water and bring to a boil. Salt the water and cook until the potatoes are fork-tender, 12-15 minutes. When tender, drain the potatoes and return to the hot pot. Mash the potatoes with the milk, cream or stock, sage, salt and pepper, and the cheese. Add nutmeg to taste and stir in the egg.
While the potatoes come to a boil, place the porcinis in a small pot and cover with the stock. Place over medium heat, bring to a boil, then reduce the heat to low and simmer to reconstitute the mushrooms.