Preheat oven to 375°F. Liberally salt and pepper chicken parts. Heat a large, oven-proof skillet. Add butter and oil and heat until butter foam subsides. Add chicken, skin-side down and cook till brown. Turn chicken over and put skillet in oven. Cook until chicken registers 160°F on a quick-read food thermometer.
Take chicken out of skillet and place the skillet back on the stove. On a low heat, carefully add the brandy or cognac to the pan. Be careful of the possible flare up of the alcohol. Reduce brandy until it is very syrupy. Add cream and reduce by half. Stir in mustard. Mix herbs together, and incorporate them in the sauce. Correct seasoning.
Each serving should be one piece of dark meat with one piece of white meat with the sauce evenly divided. Garnish with remaining herbs.
Serve the chicken with your choice of vegetable, rice and, of course, your choice of Bouchaine Vineyards wine. Enjoy on a French bistro classic!