Prepare the Chicken: Pat the chicken pieces dry with paper towels. In a small bowl, mix together the salt, black pepper, garlic powder, and onion powder. Sprinkle this mixture liberally over all sides of the chicken pieces.

Brown the Chicken: Heat olive oil or butter in a large, heavy-bottomed skillet over medium-high heat. Add the chicken pieces, ensuring not to overcrowd the pan. Brown the chicken on all sides until golden-brown (4-5 minutes per side). Remove the chicken and set aside.

Create the Roux: Lower the heat to medium-low and add the butter to the skillet. Once melted, add the flour. Whisk continuously until a smooth paste forms (roux). Cook for 3-4 minutes, or until light golden-brown, stirring constantly and ensuring not to burn it.

Thicken the Gravy: Slowly add the chicken broth to the roux, whisking continuously to avoid lumps. Cook for about 5 minutes, or until the gravy starts to thicken. Stir in the milk or half-and-half, along with the dried thyme and rosemary. Simmer for another 5-7 minutes, stirring occasionally until it reaches the desired thickness. Season with salt and pepper to your liking.

Combine Chicken and Gravy: Return the browned chicken to the skillet with the gravy. Ensure the chicken is mostly submerged. Bring to a gentle simmer, then reduce the heat to low, cover the skillet and let simmer for 20-25 minutes, or until the chicken is cooked through and tender.

Rest and Serve: Let the chicken rest in the gravy for a few minutes before serving.