Trim excess fat from chicken thighs and season them on both sides with salt and pepper. Mix the thyme and tarragon together in a ramekin and sprinkle a couple of pinches on the skin side of the thighs, as much for visual effect as for flavor.

Heat olive oil and butter in a large, lidded sauté pan over medium-high flame, swirling the pan to combine. Add chicken thighs to the pan skin down and cook until golden brown, about 5 or 6 minutes. Turn chicken, reduce heat to medium and cook for about 3 minutes. Transfer chicken to a plate, and add shallots and mushrooms to pan. Season with salt and pepper and cook, stirring frequently, for about 5 minutes.

Clear a spot in the middle of the pan and add the rest of the thyme and tarragon, along with the garlic. Cook, stirring, until fragrant, about 45 seconds. Stir to combine everything, then clear another spot in the middle. Sprinkle in flour and cook, stirring constantly, for about 1 minute. Stir everything together and add chicken stock and wine. Stir together, scraping up any browned bits. Stir in diced tomatoes and nestle chicken pieces into the mixture, along with bay leaf. Increase the heat and bring to a boil. Reduce to a simmer, cover pan and cook for 10 minutes.

Cook uncovered for an additional 20 minutes, keeping an eye on the pan and stirring sauce around chicken. If the sauce starts to reduce too much, partially cover the pan. Plate chicken, taste the sauce and adjust seasoning with salt as needed. Discard bay leaf and spoon sauce around and over chicken. Sprinkle chopped parsley over each serving.

Chicken Chasseur is traditionally served with mashed potatoes. You could also serve it with rice.