Bring water to a boil and salt it for the pasta.
Place dried porcini mushrooms in a small pot with the stock and bring to a simmer. Tun the heat down to low and steep until mushrooms are completely tender, about 10-15 minutes.
In a deep skillet, heat the EVOO over medium-high heat. Add the garlic, shallots, portobellos, shitakes, thyme, allspice and some black pepper. Cook 10-12 minutes until mushrooms are dark and tender.
Remove half the mushrooms and place them in a food processor. Add a cup of the porcini mushroom-stock broth to the processor, grind into a thick sauce and add liquid back to the skillet.