Heat the olive oil in a large skillet over medium-high heat. Add the garlic and shallots and saute until just tender. Stir in the speck and nipitella and cook until the speck is golden and crisp, about 4 minutes. Stir in the mushrooms and saute until tender, about 8 minutes.
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente. Drain well. Toss the pasta with the mushroom mixture, adding the vegetable broth to moisten. Sprinkle with the parsley and some Parmesan and toss.
You can use thyme if you can't source nipitella. Wipe the mushrooms clean with paper towels to remove any dirt and trim any discoloration from the stems with a paring knife.