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 the 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 about 1 minute until fragrant and slightly softened.
04 - Add the sliced mushrooms and fresh thyme leaves to the skillet. Increase the heat to medium-high and sauté, stirring occasionally, until the mushrooms are deeply golden brown and their released moisture has mostly 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 smoothly melted. If the sauce becomes too thick, loosen it with small additions of the reserved pasta water until the desired consistency is reached.
06 - Add the drained pasta to the skillet and toss thoroughly to coat every strand in the sauce, adding more pasta water as needed. Season with salt, pepper, and lemon juice to taste.
07 - Transfer to warm serving bowls immediately. Finish with an extra shower of Parmigiano Reggiano and a scatter of freshly chopped parsley or chives.