Pat the chicken breasts dry and season with salt, pepper, and thyme (or Italian seasoning).
Heat olive oil or butter in a large skillet over medium-high heat.
Sear the chicken for 5–6 minutes per side until golden brown. Remove from the skillet and set aside.
In the same skillet, add the mushrooms and onions. Sauté for 5 minutes until softened and slightly browned.
Stir in the garlic and cook for another minute.
Pour in the chicken broth and scrape up any browned bits from the bottom of the skillet.
If using, stir in the heavy cream or milk. Bring the sauce to a simmer.
Return the chicken breasts to the skillet, spooning the sauce over them.
Cover and let simmer for 8–10 minutes, or until the chicken is cooked through (internal temperature of 165°F)
Plate the chicken and mushrooms, spoon the sauce over the top, and serve with your favorite sides.