Preheat the oven to 325 degrees F.
Pat the meat dry and sprinkle liberally with salt and pepper. Heat 2 tablespoons of the oil in a large Dutch oven over medium-high heat and brown the meat well on all sides in 2 batches. Transfer the short ribs to a plate.
Drain off the fat from the pot and add the remaining oil. Add the carrots, celery and onions and cook until softened, 6 to 7 minutes. Stir in the flour 1 minute, then add the tomato paste and continue stirring until fragrant. Pour in the port and return the ribs to the pot. Bring to boil, then lower to a simmer and reduce the port by half, about 30 minutes. Stir in the stock, thyme, sage, rosemary, marjoram, garlic and the handful of parsley. Return to a boil, then cover and place in the oven, 2 hours 30 minutes.
As soon as you remove the beef from the oven, bring the potatoes to a boil in salted water and cook until tender.
Transfer the beef to a platter and strain the sauce. Skim the fat by either quickly placing ice cubes into a metal ladleful of sauce (the fat will stick to the bottom of the ladle), or by carefully spooning the fat from the surface with a large spoon. Return the sauce to the heat to reduce and thicken a bit while the potatoes cook. Season the sauce with salt and pepper.
Drain the potatoes and return to the hot pot. Mash the potatoes with the cream and butter and season with salt, pepper and nutmeg.
Serve the ribs with the potatoes and top with the sauce, pomegranate seeds, if using, and the chopped parsley. Serve with steamed green beans or green salad.
For a make-ahead meal, cool and return the meat to the sauce. Reheat by gently bringing to room temperature and heating on the stovetop over medium heat. Cook the potatoes as the meat is reheating.