01 - Bring a large pot of generously salted water to a rolling boil. Introduce the pasta and cook according to package directions until perfectly al dente. Reserve approximately 120 ml (1/2 cup) of the starchy pasta water before draining the pasta thoroughly.
02 - Concurrently, heat 2 tablespoons of olive oil and the butter in a large skillet over medium-high heat. Add the finely chopped shallots and sauté for 2 minutes until they become translucent and tender. Incorporate the minced garlic and continue to cook for an additional 30 seconds until fragrant, taking care not to burn.
03 - Add the sliced chestnut mushrooms and thyme to the skillet. Sauté, stirring occasionally, for 7 to 8 minutes. Continue cooking until the mushrooms are deeply golden brown and have released their moisture. Season generously with salt and freshly ground black pepper.
04 - While the mushrooms are cooking, prepare the rosemary oil. In a small saucepan, gently warm 60 ml of extra-virgin olive oil with the fresh rosemary sprigs over low heat for 5 to 8 minutes. Heat just until the oil is fragrant, ensuring it does not reach a sizzling point. Remove from heat and allow it to infuse.
05 - Add the drained pasta directly to the skillet containing the sautéed mushrooms. Toss the pasta and mushrooms together to combine evenly. Gradually incorporate the reserved pasta water, a little at a time, to emulsify and create a silky, cohesive sauce that coats the pasta.
06 - Carefully remove the rosemary sprigs from the infused oil. Drizzle the fragrant rosemary oil generously over the pasta and mushrooms. Toss everything together thoroughly to ensure the oil is well distributed.
07 - Serve the pasta immediately. Garnish each portion with grated Parmesan cheese (or vegetarian alternative), fresh lemon zest, and a scattering of chopped fresh parsley, if desired.