Heat 2 tablespoons of EVOO in a large skillet over medium-high heat. Season the chicken chunks with salt and ground black pepper then sauté them on all sides in the hot pan until golden brown. Remove from skillet and reserve on a plate. (If using chopped rotisserie chicken, skip this step!)
Add the butter, onion, carrot, celery and garlic to the same skillet and cook, stirring occasionally, until the vegetables are tender, 5-6 minutes.
Sprinkle in the flour and cook until light brown, about 1 minute. Whisk the chicken stock into the veggie-butter-flour mixture and bring it to a boil. Simmer the gravy until thickened, 2-3 minutes, then return the browned chicken back to the pan and mix to combine.