Loosen the skin on each side of the chicken breasts and insert up to six mixed herb sprigs. With the remaining herbs, strip off enough leaves to make 3/4 cup (1/2 a cup will be used in the marinade and a 1/4 cup as garnish). Reserve the sprigs, stems, and any leftover leaves for the grilling.
In a small bowl, combine olive oil, wine, shallots, 1/2 a cup herbs, sea salt (it really does make a difference), and fresh pepper. Pour into a large ceramic or glass bowl. Add the chicken breasts and marinate in the refrigerator for 2 hours, turning the chicken 3 or 4 times.
Half an hour before grilling:
Remove the chicken from the refrigerator. Strain out the herbs and reserve the marinade. Also soak the grapevine cuttings in cold water to cover. Place the reserved grilling leaves, sprigs and stems in water to cover. Light a hardwood lump charcoal fire in a grill with a cover.
When the coals are ready, sear the chicken breasts on all sides for a total of 5 minutes, basting several times with the marinade. Drain the grapevine cuttings and sprinkle them evenly over the coals. Baste the chicken, cover, partially close the vents, and cook for 10 minutes. Baste, turn, and baste the chicken again. Drain the herb leaves, sprigs, and stems and sprinkle them over the coals. Cover the grill and cook the chicken 10 minutes longer (a total of 20 minutes), or until the flesh is opaque throughout when cut into with a knife.
Transfer the chicken from the grill to a plate, cover with aluminum foil, and hold in a very low oven for up to 20 minutes.
Pour the leftover marinade into a small saucepan and whisk at a boil until the liquid is reduced to a thick syrup; watch carefully to avoid burning. Whisk in the chicken broth and cream and boil again until the mixture has thickened; whisk in the mustard and remove from the heat.
Cut each breast into diagonal slices 1/2 an inch thick. Whisk any juices from the chicken plate into the sauce. Pour a puddle of sauce onto the plate, arrange the chicken slices in a fan shape over the sauce, sprinkle the edge of the plate with herb leaves, and serve.
Serve the chicken with grilled red potatoes (cut in half); grilled red onion wedges and grilled zucchini slices sprinkled with balsamic vinegar (you can hold the cooked vegetables in a warming oven); and a Sauvignon Blanc.