Pre heat oven to 400 degrees.
Sprinkle chicken with salt and pepper.
Heat vegetable oil in skillet until almost smoking and add chicken breasts skin side down and cook until skin is crisp and well browned - about 8 minutes.
Turn chicken breasts over in skillet and cook for an additional 5 minutes. After place on bake pan and set aside.
Pour off all but 2 tablespoons of the fat and add mushrooms and cook until browned - about 6 to 8 minutes. Add the shallots and cook an additional minute.
Remove pan from heat and add brandy. Allow to sit for 15 seconds before lighting brandy in pan with chimney match. Return pan to fire and cook until flames subside. Add the wine and scrape the fond on the bottom of the pan for about 3 minutes.
Move the chicken to the oven until reaches 160 degrees - about 20 minutes.
Add the broth and tomatoes to the pan with the mushrooms and allow to cook down for about 25 minutes.
After sauce has reduced, add the butter one tablespoon at a time until melted. Add parsley and tarragon to sauce and stir to combine.
Serve the chicken with the sauce over the chicken.