Heat about a tablespoon of fat in a medium skillet over medium heat. Add the mushrooms, season with salt and pepper and cook, stirring occasionally, until the mushrooms are tender, about 10 minutes. Set the mushrooms aside to cool.
Combine the thyme and rosemary and rub the mixture over the boned (skinless) side of the chicken. Season the skin side with salt and pepper. Heat the remaining 2 tablespoons fat in a large ovenproof skillet, over medium-high heat. Working in batches if necessary, brown the chicken, skin-side down until the skin is crisp, 7 to 10 minutes.
Lay a slice of foie gras (if using) over the thigh of each chicken. Fold the breasts over the thighs so that the breasts sit on the thigh and leg meat and the skin is on the outside. Fit a metal ring over each chicken-half to hold the meat in a compact shape.
Transfer the skillet to the oven and roast, basting the chicken several times with pan juices. Cook until the thighs reach and internal temperature of at least 140 degrees F. and the juices run clear, about 20 minutes. Transfer the chicken to a plate and set aside to rest for 10 minutes in a warm place.
Pour off all but about 2 tablespoons the fat from the skillet. Add the mushrooms, truffle oil, and cream and heat over medium-high heat, scraping any browned bits from the pan's bottom. Simmer until the cream reduces enough to coat the back of a wooden spoon, then season, to taste, with salt and pepper.
Remove the molds from the chicken and arrange on warm plates. Spoon the sauce around the chicken and serve with French green beans, carrots, and ratatouille if desired.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.