Preheat the oven to 350.

Season the chicken on both sides with 1/2 teaspoon salt and 1/4 teaspoon pepper.

Heat the vegetable oil over medium-high until it just starts to shimmer and smoke.

Add the chicken, skin side down and don't move it for 6 minutes. Turn it over and cook 6 minutes more--just so that the chicken gets a little brown color on it. Transfer it to a 5-quart pot with a tight fitting lid.

To the remaining oil in the skillet, add the onions and cook over medium until they start to soften--about 2 to 3 minutes. Sprinkle over 1/4 teaspoon each of salt and pepper. Transfer the onions to the pot with the chicken.

In the same skillet over medium heat again, add 1 more tablespoon vegetable oil and the flour. Stir constantly 1 minute until no pockets of flour remain then add the broth, white wine vinegar and remaining salt and pepper. Simmer and stir constantly until the sauce thickens--about 5 to 6 minutes. Taste it to see if it needs more salt or pepper.

Pour the sauce over the chicken and onions. Add the thyme leaves and cover. Bake 30 minutes.

After 30 minutes, remove from the oven and add the mushrooms. Cover and bake again an additional 20 to 30 minutes until the chicken is cooked through. Serve warm with toast.