Preheat the oven to 300°F (150°C).

In a spice grinder, combine the toasted mustard seeds and cracked black pepper. Grind until finely crushed.

Season the beef short ribs generously with salt and then rub the mustard seed and black pepper mixture all over the ribs.

In a large oven-safe pot or Dutch oven, heat the olive oil over medium-high heat. Add the short ribs, searing them on all sides until browned (about 3-4 minutes per side). Remove the ribs and set aside.

In the same pot, add the chopped onion and cook until softened, about 5 minutes. Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.

Pour in the beef broth, pomegranate juice, and balsamic vinegar. Add the brown sugar and stir to combine.

Return the short ribs to the pot, ensuring they are submerged in the liquid. Bring to a simmer.

Cover the pot and transfer it to the preheated oven. Braise the ribs for 2.5 to 3 hours, or until tender and falling off the bone.

Once cooked, remove the pot from the oven and transfer the short ribs to a plate, covering them with foil to keep warm.

Strain the cooking liquid through a fine mesh sieve into a saucepan. Discard solids and bring the liquid to a boil over medium-high heat. Reduce the sauce by half until it thickens slightly.

Adjust seasoning with salt if needed.

Serve the short ribs drizzled with the pomegranate-balsamic gravy, and garnish with chopped fresh parsley.