Preheat an oven. Place quartered mushrooms and halved garlic cloves on a rimmed baking sheet, then drizzle with olive oil. Season with Kosher salt and freshly ground black pepper. Scatter butter and thyme sprigs on top. Transfer to the preheated oven and roast until the mushrooms are tender.
Bring a large pot of water to a rapid boil. Season generously with Kosher salt. Add dried gnocchi, then cook until they float to the top. Reserve the cooking water, then drain. Set gnocchi aside.
Heat butter in a large skillet over medium heat. Add chopped shallot then cook, stirring occasionally, until softened. Add thinly sliced garlic, then cook.
Stir in shredded rotisserie chicken, the roasted mushrooms, cooked gnocchi, mascarpone cheese, and reserved pasta water. Increase the heat to medium-high, then stir until the cheese has melted. Add additional reserved cooking water to create more of a sauce if you like.
Add arugula, then stir to combine or until just barely wilted. Divide evenly between bowls. You can add a little more arugula on top for extra greens. Drizzle each bowl with a little truffle oil, then top with grated Parmesan cheese and lots of freshly ground black pepper. Serve immediately!