Warm 2 tablespoons of butter in a medium sauté pan over medium heat and add the whole peeled shallots. Season with salt and pepper and sauté, without color – stirring frequently for 5-7 minutes. Add the Port and reduce until dry. Add the red wine and reduce again until dry. Add one cup of the chicken stock, bring to a boil and lower the heat so the liquid simmers. Cook until the liquid coats the back of a spoon and the shallots are tender when pierced with a knife. Set aside for the moment in a warm place.
Warm the remaining 2 tablespoons of butter in a medium sauté pan over medium heat. Add the carrots, season with salt and pepper, and sauté, without color – stirring frequently, for 5-7 minutes. Add the remaining 2 cups of chicken stock and bring the stock to a boil. Lower the heat so the liquid simmers and braise the carrots until nearly all the liquid evaporates from the pan and the carrots are tender and glazed. Set aside for the moment in a warm place.
Preheat the oven to 450°F.
Warm the oil in a small roasting pan or Dutch oven over high heat. Season the beef on both sides with salt and pepper and, when the oil is very hot, add the meat to the pan. Brown the meat evenly, approximately 5-7 minutes on each side, place the rosemary and thyme on top and then transfer the pan to the oven. Roast for approximately 20-25 minutes or until a meat thermometer inserted into the center of the meat reads 110°F, for medium rare. Remove the chop from the pan, transfer to a warm plate and let rest for 5 minutes.
Spoon the carrots and shallots – leave the Port and red wine shallot glaze in the pan – into a medium decorative casserole and rewarm in the oven for 5 minutes while the meat is resting. Place the shallot glaze over low heat and bring just to a boil. Place the chop on top of the vegetables, drizzle the meat with some of the shallot glaze and sprinkle with some fleur de sel. Serve immediately.