Season chicken on both sides with salt and pepper.
Heat 1 T butter in a heavy large skillet or braiser. Add chicken skin side down and cook until skin is golden, about 5 minutes. Turn and cook on other side 5 minutes more. Transfer chicken to a plate (chicken will further cook with sauce later).
Add shallots and garlic to pan and cook for 5 minutes to soften. Add tomato paste and stir, cooking for 1 minute. Increase heat to high and add vinegar. Reduce by half, then add wine. Continue to simmer for 5 minutes, then add in stock. Stir, then reduce sauce for 10 minutes.
Lower heat and add thyme (or tarragon). Return chicken to sauce, cover pan and allow to cook for 15-20 minutes, or until chicken is cooked through (165 F on a digital thermometer).
Remove chicken from pan to a plate again and stir in heavy cream. Simmer sauce for 15 minutes, until sauce has thickened to the "nappe" stage (submerge back of a spoon in the sauce, run index finger down the spoon thru sauce, if line stays clean, sauce is ready). Season to taste with salt and pepper. Stir in remaining T butter if using. Return chicken to pan and allow to warm through.
Garnish with chopped parsley. Serve over buttered noodles or rice.
