Pat the short ribs dry with paper towels. Heat a large heavy-bottom skillet over medium-high heat and add 2 tablespoons olive oil. Season the ribs with a good pinch of salt and pepper and sprinkle 2 tablespoons of the brown sugar over them. Sear the ribs until browned on all sides, about 1 minute per side. Transfer the seared ribs to the crockpot.

Pour any browned bits and drippings from the skillet into the crockpot.

Add the thinly sliced onion, minced garlic, and chopped carrots to the crockpot around and on top of the ribs.

Sprinkle the remaining brown sugar (1/4 cup) over the vegetables and ribs. Add 1 1/2 cups pomegranate juice, 1/3 cup soy sauce, 1 tablespoon fresh thyme, 1 tablespoon fresh rosemary, 1/4 teaspoon cayenne pepper, and 1/4 cup fresh parsley. Scatter the arils from one pomegranate over everything.

Cover and cook on low for about 8 hours, or on high for 5–6 hours, until the meat is very tender and falling off the bone. If possible, rotate the short ribs once or twice during cooking for even braising.

During the last 30 minutes of cooking, remove the lid and set the crockpot to high (if already on high, simply remove the lid) to allow the sauce to reduce and thicken slightly.

While the ribs are finishing, make the polenta: bring 2 cups chicken broth and 2 cups milk to a boil in a medium saucepan. Reduce the heat to medium and slowly whisk in 1 cup polenta. Cook, stirring frequently, until the polenta is soft and thick, about 15–20 minutes. Keep the polenta warm.

Just before serving, stir 4 ounces mascarpone and 2–4 tablespoons butter (to your taste) into the polenta. Season the polenta with 1/4 teaspoon salt and 1/4 teaspoon pepper. If the polenta seems too thick, add an extra tablespoon of butter or a splash of milk to loosen it.

To serve, spread a bed of polenta on each plate, place short ribs on top, and spoon the crockpot sauce over the ribs. Garnish with additional pomegranate arils.