Season and Dredge the Chicken: Pat the chicken dry and season generously with Cajun seasoning. Place the flour in a shallow dish with a little more Cajun/creole seasoning and lightly dredge each piece, shaking off the excess. This helps the chicken brown and will naturally thicken the gravy later.
Sear the Chicken: Heat a large skillet over medium-high heat. Add the oil (ideally I shoot for about a ½ -1 inch of oil). Working in batches if needed, sear the chicken skin-side down first until golden brown, about 4–5 minutes per side. The chicken does not need to be cooked through. Remove the chicken and set aside.
Build the Trinity: Reduce heat to medium. In the same pan, add the onion, bell pepper, and celery. Cook for 5–7 minutes, stirring occasionally, until the vegetables soften and begin to brown. Add the garlic and cook for 30 seconds until fragrant.
Make the Roux: Sprinkle the flour over the vegetables and stir to combine with the pan drippings. Cook for 2–3 minutes, stirring constantly, until the flour takes on a light to medium brown color and smells slightly nutty. Note: continue to add flour in batches until the roux thickens to your desired consistency. Build the Gravy: Slowly pour in the warm chicken stock while stirring to prevent lumps. Add Worcestershire sauce and additional Cajun seasoning to taste. Bring to a gentle simmer and cook for 3–5 minutes until the gravy thickens enough to coat a spoon. If the gravy thickens too much, simply add more broth to help thin it out.
Smother the Chicken: Return the chicken to the pan, skin-side up. Reduce heat to low, cover, and simmer gently for 25–35 minutes, or until the chicken is tender and cooked through. Breasts should reach 160–165°F and thighs/drumsticks should reach 170–180°F.
Stir in butter, if desired. Taste and adjust seasoning. Garnish with parsley and serve hot over grits, with plenty of the Cajun gravy spooned over the top.