1. Adjust oven rack to middle position; heat oven to 400°F. Sprinkle chicken pieces evenly with salt and pepper. Heat oil in 12-inch skillet over medium-high heat until almost smoking. Add chicken pieces skin side down and cook without moving them until skin is crisp and well browned, 5 to 8 minutes. Using tongs, turn chicken pieces and brown on second side, about 5 minutes longer. Place browned chicken skin side up on rimmed baking sheet and set aside.

2. Pour off all but 2 tablespoons fat from pan. Add mushrooms and cook over medium-high heat until mushrooms start to brown, 6 to 8 minutes. Reduce heat to medium and add shallots; cook until softened, about 1 minute longer.

3. Remove pan from heat and add brandy; let stand until brandy warms slightly, about 10 seconds. Wave lit chimney match over skillet until brandy ignites. Return pan to medium-high heat and shake skillet until flames subside. Add wine; using wooden spoon, scrape browned bits from pan bottom. Simmer briskly until reduced to glaze, about 3 minutes.

4. Add broth and tomatoes and simmer over medium-high heat; simmer briskly until liquid, mushrooms, and tomatoes measure 1 1/2 cups, about 25 minutes.

5. While sauce simmers, place chicken in oven; roast breasts until internal temperature reaches 160°F on instant-read thermometer, about 15 to 20 minutes. Transfer breasts to serving platter and tent loosely with foil. Continue to roast thighs until internal temperature reaches 175°F, about 10 minutes longer, then transfer to platter with breasts.

6. When sauce is properly reduced, whisk in butter, one piece at a time, until melted and incorporated. Add parsley and tarragon and adjust seasoning with salt and pepper. Spoon sauce over chicken and serve immediately.

Serves 4