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.
Remove the porcinis from the stock with a slotted spoon, chop and add to the skillet. Ladle in remaining stock, discarding the last few spoonfuls at the bottom of the pot where the grit from the mushrooms has settled. Season the sauce with salt to taste and remove thyme stems.
Drain pasta when it's al dente and add it to the mushroom sauce to absorb flavor. Add a couple handfuls of Pecorino and toss to combine. Adjust seasonings, spoon into bowls and top with nuts, shredded arugula and more cheese. Drizzle a little truffle oil over it if you want to go into true 'shroom madness!