Bring a large pot of water to a boil and generously salt it. Cook the fettuccine according to package directions minus 1 minute, reserving 1 cup of pasta cooking water before draining.
While the pasta cooks, heat a large skillet over medium heat and add 2 tablespoons of the butter and the olive oil.
Add the sliced mushrooms and cook, stirring occasionally, until they are 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 everything briskly with tongs, adding reserved pasta water a little at a time (about 1/2 to 3/4 cup) until the sauce is creamy and coats the pasta. Stir in the grated Parmesan.
Add the chopped spinach and toss gently until wilted. Remove the skillet from the heat and taste, adjusting salt and pepper as needed.
Serve immediately with extra Parmesan and a sprinkle of fresh parsley if desired.