Season the chicken breasts with salt, pepper, garlic powder, and onion powder. Dredge each breast in flour, shaking off the excess.
In a large skillet, heat the vegetable oil over medium heat. Add the chicken breasts and cook for about 5-7 minutes on each side, until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chicken broth, milk, Worcestershire sauce, thyme, and cayenne pepper (if using). Stir well to combine, scraping up any browned bits from the bottom of the skillet.
Bring the mixture to a simmer and let it cook for about 5 minutes, allowing it to thicken slightly.
Return the chicken to the skillet, spooning the gravy over the top. Cover and let it simmer for an additional 5 minutes to heat through.
Serve the chicken with the gravy over rice or mashed potatoes.