If you plan on serving the over fettuccine, start the water before you do anything else to allow the pasta to cook while you prepare the meal.
Slice the chicken breasts in half. If there are parts of the chicken that remain thick (about more than a 1/2 inch), pound them thin. Season the chicken with salt and pepper on both sides. Dredge in the flour.
In a larget skillet, heat 2 tablespoons of extra virgin olive oil over medium heat. Add the sliced chicken to the pan and cook for about 5 to 6 minutes on each side or until a meat thermometer reads 165 degrees.
Remove the chicken from the pan and cover loosely with aluminum foil.
Add the butter to the skillet and melt. Add in the mushrooms and the garlic. Cook until the mushrooms are soft, about four minutes.
Stir in the flour througly, so the mushrooms are fully coated. Slowly pour in the beef broth, scraping up browned bits at the bottom. It works best if you pour in a little, stir it in to combine, and then a little more.
Season with Worcestershire sauce, ground mustard, salt and pepper. Bring to a simmer. Add in the spinach. Cook until the sauce thickens and reduces by almost half, about six minutes, stirring occasionally. Stir in the heavy cream. Taste the sauce and season with more salt and pepper as necessary.
Return the chicken to the pan. Spoon the sauce and mushrooms over the chicken and serve over fettuccine.