Put the chicken thighs on a rimmed baking sheet or baking dish. Sprinkle the salt on both sides of chicken. Refrigerate, skin side up and uncovered up to 24 hours ahead. This will season the chicken and help the skin to crisp and brown. If you're short on time, season with the salt and let it sit at room temperature 15 minutes then proceed with the recipe.
Preheat the oven to 425 (220C) degrees.
Heat a large (12-inch) wide pan with at least 2-inch sides over medium high heat. Add the olive oil to the pan, and when it shimmers add the chicken, skin side down. Cook undisturbed for 10 minutes, watching that the pan doesn't get too hot and adjusting the heat accordingly, until the skin is a rich golden brown. Turn chicken and cook the other side 2 minutes. Remove chicken to a plate.
Pour off all but about a teaspoon of the fat in the pan, and stir in the shallot and garlic. Cook about 30 seconds, then pour in the white wine and vinegar, scraping the pan to remove the brown bits. Add the tomato paste, mustard, thyme, bay leaves and broth. Bring to a simmer then return chicken to the pan, skin side up.
Transfer the pan to the oven and roast 25 minutes, until the sauce is bubbling and the chicken is cooked through. *Note: If you notice the pan juices are reducing quickly after 10-15 minutes, add up to ½ cup more liquid to the pan.
Sprinkle the chili over the chicken, if using, and remove the bay leaves. Serve warm with the pan juices spooned over.
I use Diamond Kosher salt, which has a larger grain than other brands like Morton, and isn't as salty by volume. To season the chicken with a different brand, reduce the amount of salt to 2 teaspoons.
Store leftovers in the refrigerator up to a week. They taste even better!