This earthy dish calls on the rustic charms of southwestern France. A French classic that never seems to go out of style, the name, literally "hunter's chicken," harks back to a time when game birds and mushrooms from the woods were a natural autumn combination.
In a large, deep frying pan, heat the oil over moderately high heat.
Season the chicken with 1/4 teaspoon each of the salt and pepper and add to the pan.
Cook until browned, turning, about 8 minutes in all. Remove. Pour off all but 1 tablespoon fat from the pan.
Add the butter to the pan and reduce the heat to moderately low.
Add the onion and cook, stirring occasionally, until translucent, about 5 minutes.
Raise the heat to moderately high. Add the mushrooms, garlic and 1/4 teaspoon of the salt. Cook, stirring frequently, until the vegetables are browned, about 5 minutes.
Add the flour and cook, stirring, for 30 seconds.
Stir in the vermouth and bring back to a simmer.
Stir in the broth, tomatoes, thyme, and the remaining 1/2 teaspoon salt.
Add the chicken and any accumulated juices.
Reduce the heat; simmer, covered, until the chicken is done, about 10 minutes.
Stir in the parsley and the remaining 1/4 teaspoon pepper.