Bring a large pot of water to a rolling boil and generously salt it. Cook the fettuccine according to package directions minus 1 minute for al dente. Before draining, reserve 1 cup of the pasta cooking water, then drain the pasta.
While the pasta cooks, heat a large skillet over medium heat and add 2 tablespoons butter and the olive oil.
Add the sliced mushrooms and cook, stirring occasionally, until golden brown and their liquid has evaporated, about 5 minutes.
Season the mushrooms with salt, pepper, and the Italian seasoning. Add the remaining 1 tablespoon butter and the minced garlic, and cook 1–2 minutes until fragrant and lightly golden.
Reduce heat to low and add the Boursin cheese, chopped rotisserie chicken, and the hot drained pasta to the skillet.
Toss briskly with tongs while gradually adding reserved pasta water (start with about 1/2 cup and add up to 3/4 cup as needed) until the sauce is creamy and coats the pasta. Stir in the grated Parmesan.
Add the chopped spinach and gently toss until wilted, then remove the skillet from the heat. Taste and adjust seasoning with more salt and pepper if needed.
Serve immediately with extra Parmesan and a sprinkle of fresh parsley, if desired.
