Prepare the Chicken:

1. Season the Chicken: Pat the chicken thighs or breasts dry with a paper towel. Season generously with salt, pepper, and a sprinkle of dried thyme and rosemary.
2. Cook the Chicken: Heat olive oil or butter in a large skillet over medium heat. Once hot, add the chicken and cook for 6-7 minutes per side, or until golden brown and cooked through. Remove from the skillet and set aside.

Make the Gravy:

3. Sauté the Aromatics: In the same skillet, add the chopped onion and garlic, cooking for about 2-3 minutes until softened and fragrant.
4. Create the Roux: Sprinkle the flour over the onions and garlic and stir to combine. Cook for 1-2 minutes to remove the raw flour taste, creating a thick roux.
5. Add Chicken Broth: Slowly pour in the chicken broth while stirring constantly to prevent lumps from forming. Scrape the bottom of the skillet to release any brown bits, which will add flavor to the gravy.
6. Season the Gravy: Stir in the dried thyme and rosemary, and adjust the salt and pepper to taste. Bring the mixture to a simmer, letting it cook for about 5-7 minutes until thickened.

Finish the Dish:

7. Add Milk or Cream: Stir in the milk or cream, and continue to simmer for another 3-5 minutes until the gravy is smooth and creamy.
8. Return the Chicken: Place the cooked chicken back into the skillet with the gravy, spooning the sauce over the chicken to coat it. Let it simmer for another 5-10 minutes, allowing the chicken to absorb the flavors of the gravy.

Serve:

9. Serve and Garnish: Serve the Homestyle Chicken and Gravy over mashed potatoes, rice, or biscuits. Garnish with freshly chopped parsley for an added touch of color and flavor.