Make the chicken. Add the chicken and 1 tablespoon of the salt to a large bowl. Fill with cold water, cover, and refrigerate for at least 1 hour or up to overnight.
Preheat the oven to 450°F with a rack in the center position.
In a small bowl, combine the remaining 1 teaspoon salt, pepper, garlic powder, onion powder, paprika, and brown sugar (if using).
Transfer the chicken to a plate and pat dry. Brush with the olive oil and season all over with the spice rub. Arrange the chicken in a 9x13-inch baking dish and bake for about 18 minutes, or until the internal temperature of the chicken reaches 165°F on an instant-read thermometer. Turn the oven to broil. Broil until the tops are golden, about 3 minutes.
Meanwhile, make the mustard cream sauce. Heat the olive oil in a medium skillet over medium heat. Once the oil is glistening, add the shallot and cook, stirring, until translucent, about 5 minutes. Stir in the white wine and cook, stirring, until reduced by half, about another 3 minutes. Stir the whole grain mustard and Dijon mustard until smooth, then slowly pour in the chicken stock and the heavy cream, stirring constantly.
In a small bowl, combine the butter and flour to create a roux. Add the roux to the sauce and bring to a simmer. Cook, stirring, until thickened enough to coat the back of the spoon, about 4 minutes.
Serve the chicken with the mustard cream sauce, sprinkled with parsley, if using.