Heat oven to 375°F. Season both sides of chicken with salt and pepper. Heat oil in a large Dutch oven, or 12-inch skillet with a lid, over medium heat.
Sear chicken skin side down until golden brown, about 5 minutes, without moving so the fat renders and skin crisps. Once nicely browned, turn and sear the other side for 3 to 4 minutes. Transfer to a platter and set aside.
In the same pan, cook the shallots over medium-low heat until softened, about 5 minutes. Add the garlic and cook another minute until fragrant.
Add the wine, stock, mustard and thyme to the pan and bring to a rapid simmer. Return the chicken to the pan with any juices, cover with lid, and transfer to the oven. Bake for 30 minutes or until chicken is cooked through and reaches 165°F internal temperature.
Once the chicken is done, remove from the oven and turn the broiler on Hi. Transfer chicken to a rimmed baking sheet, skin-side up, and return the pan to the stove top.
Add the cream to the sauce and simmer for 5 minutes or until sauce thickens. While simmering the sauce, place chicken under the broiler to crisp skin, 3 to 4 minutes. (You can remove the thyme stems at this point.) Serve chicken with the sauce and garnish with fresh parsley.
Make it without alcohol—substitute 2 tablespoons of apple cider vinegar for the wine and increase the chicken stock to 1 1/2 cups total.
If using boneless, skinless chicken breasts, skip the step of continued cooking in the oven. Brown the chicken breasts until the internal temperature reaches 165 degrees or until no longer translucent inside. Serve with the finished sauce.