Toast the pasta: Preheat oven to 350°F Put pasta on a baking sheet, coat it with one tablespoon of the olive oil (using your hand, rub the and then spread it out in a single layer. Bake until the pasta is golden to russet color, about 10-13 minutes. Do not let scorch. Let cool.
Make the broth: Wrap up the mushroom stems, parsley stems, garlic, thyme, and peppercorns in a square of cheesecloth and set the sachet aside.
Heat the remaining 2 tablespoons oil in a large skillet over medium-high heat. Add the shallots and cook, stirring occasionally until soft and golden, about 10 minutes. Add the sliced shiitakes and cook until they begin to brown, about 10 minutes. Season the mushrooms with salt, then transfer them to a large saucepan.
Add the sachet, the stock, and 2 cups of water to the mushrooms. Bring to a simmer and cook until the broth has a nice mushroom taste, about 15 minutes. Discard the sachet.
Break the pasta in half and add it to the simmering broth. Cook just until the pasta is done, about 5 minutes.
Adjust the seasoning with salt and pepper if necessary, then ladle the broth and pasta into bowls. Serve garnished with parsley leaves and chives. Add spinach or braised bok choy if desired.