Put a large pot of salted water on to boil for the pasta.
Heat 2 tablespoons of the butter along with the olive oil in a large skillet over medium heat. Add the onion and sauté until soft and translucent, 4 to 5 minutes.
Add the mushrooms and cook, stirring frequently, until they have given off most of their liquid and are starting to brown, 4 to 5 minutes longer.
Add the garlic and continue cooking until the mushrooms are nicely browned. Season to taste with salt and pepper, then deglaze the pan with 1/2 cup of the broth, scraping up any browned bits that may have accumulated on the bottom.
Whisk the cornstarch into the remaining 1/4 cup of chicken broth until smooth. Add it to the mushroom mixture and bring the liquid to a simmer.
As soon as the sauce begins to thicken, add the turkey and combine well. Continue cooking for about 30 seconds to heat the turkey, then stir in the cream and thyme. Remove the pan from the heat and cover to keep warm.
Cook and drain the fettuccine according to package directions, then return it to the pan, add the remaining 2 tablespoons butter and toss to coat. Add the mushroom mixture and combine well. Taste and adjust the seasoning if needed and serve immediately.
Tips for Making This Recipe
This recipe can just as easily be made with leftover or store-bought rotisserie chicken.