In a small bowl pour 1 1/2 cups hot water over dried porcini mushrooms and let it sit until the mushrooms get soft, about a half-hour.
Transfer mushrooms to a cutting board and chop into small pieces, leave any liquid behind and reserve for future use.
Melt butter in a large pot over medium-high heat
Add shitake and button mushrooms and saute for about 10 minutes
Add leeks and garlic and saute for 5 minutes
Add wine, thyme, and porcini mushrooms. Cook until most of the wine is evaporated about 5 minutes and stir it occassioanlly.
Transfer all these items to a large bowl. Mix in bread, egg and season with salt and pepper as needed.
Preheat oven to 350 degrees
Grease a 13x9x2-inch baking dish
Add in some of the reserved mushroom liquid to keep the dish moist.
Transfer stuffing to baking dish
Bake for about 40 minutes, uncovered, and until it is heated all the way through.