01 - Bring a large pot of generously salted water to a rolling boil. Add the fettuccine and cook until al dente according to package directions. Reserve 1 cup of starchy pasta water before draining.
02 - While the pasta cooks, heat the olive oil and butter in a large skillet over medium heat. Allow the butter to melt and foam, swirling the pan occasionally, until it turns a deep golden-brown and releases a nutty aroma, about 3 to 4 minutes.
03 - Add the finely diced shallot and minced garlic to the browned butter. Sauté for 1 minute until fragrant and softened.
04 - Add the sliced mushrooms and fresh thyme leaves. Increase the heat to medium-high and sauté until the mushrooms are deeply golden and their released moisture has evaporated, about 6 to 8 minutes.
05 - Pour in the heavy cream and bring to a gentle simmer. Reduce the heat and stir in the grated Parmigiano Reggiano until melted and smooth. If the sauce is too thick, incorporate reserved pasta water a splash at a time until the desired consistency is reached.
06 - Add the drained pasta to the skillet and toss to coat evenly in the sauce, adding more pasta water as needed to achieve a silky finish. Season with salt, freshly ground black pepper, and lemon juice if using. Taste and adjust seasoning.
07 - Serve immediately in warm bowls, garnished with additional Parmigiano Reggiano and a sprinkle of fresh parsley or chives.