Preheat the oven to 350°.
Season both sides of the chicken with 1 teaspoon of salt and the black pepper.
In a large, deep non-stick skillet or Dutch oven set over medium-high heat, add the olive oil. Once the oil is shimmering, add the chicken thighs, skin-side down, and reduce the heat to medium.
Cook until the skin is golden brown, 8 to 10 minutes. Use a metal spatula to turn the thighs over and cook about 1 minute longer. Transfer the chicken skin-side up to a plate.
Add the celery, onion, garlic, raisins, bay leaf, rosemary, thyme and remaining salt to the skillet. Cook, stirring often until the onions are soft, about 5 minutes. Increase the heat to medium-high and stir in the mustard, then pour in the wine and orange oil.
Cook until the wine is slightly reduced, 3 to 5 minutes, then add the broth. Move chicken to an oven safe roasting dish and pour the skillet ingredients over the chicken.
Cover the pan and braise the chicken in the oven for 25 minutes. Uncover and cook 20 minutes more. Transfer the chicken to a platter and set aside.
Set the baking dish over medium-high heat and add the cream. Cook, stirring occasionally, until the sauce thickens, 3 to 4 minutes. Turn off the heat, remove the bay leaf, rosemary, and stir in the chopped celery leaves and parsley leaves. Spoon the sauce over the chicken and serve.