Heat oil in a large skillet over medium heat. Add the onions, garlic, and mushrooms. Saute until onions are soft, about 3 to 5 minutes.
In a small bowl, whisk the chicken broth and 3 Tablespoons of flour together until blended. Whisk in the cream {or CashewMilk} and set aside.
Stir the remaining 3 Tablespoons of flour into the skillet {it will form a thick paste}. Add the broth mixture and bring to a boil, stirring occasionally. Sauce should begin to thicken.
Reduce heat and add the wine, salt, pepper, nutmeg, and tarragon. Continue to simmer, stirring occasionally for 25 minutes.
Stir in the sour cream/Greek yogurt and continue to simmer for an additional 5 minutes.
Add the chicken breasts to the skillet, cover with foil and bake in a preheated 350 degree oven for 20 minutes.
Serve chicken over a bed of Fettuccine Alfredo with the creamy mushroom sauce poured on top. Garnish with parsley and grated Parmesan if desired.
Notes
The sauce will thicken as it cools. My sauce looks thinner because I used CashewMilk. If you use heavy cream, your sauce will be thicker and creamier.
Using sour cream versus Greek yogurt will also create a thicker, creamier sauce.
I used 2 pounds of chicken breasts, and they are very thick! You can place the chicken breasts between two sheets of plastic wrap and beat them with a rolling pin to achieve a thinner, more uniform thickness if desired. Then cut the breasts in half for 6 servings. I was being lazy and skipped this step.
If you do not want to use wine, substitute additional chicken stock.
If you hate tarragon for some reason, substitute thyme.
For completely dairy-free, substitute canned coconut milk and dairy-free sour cream. It will not be as thick and creamy, and yes it will taste like coconut. Add an extra Tablespoon of tarragon to help mask the flavor.
I do not recommend using almond or rice milk in this recipe, they are way too thin and watery. If you must, you will need to add additional flour or cornstarch to thicken your sauce.