Preheat your oven to 300°F (150°C).

Season the short ribs generously with salt and black pepper.

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

In the same pot, add the sliced shallots and sauté until softened and lightly caramelized, about 5-7 minutes. Add the minced garlic and cook for an additional 1-2 minutes until fragrant.

Pour in the pomegranate juice and beef broth, scraping up any browned bits from the bottom of the pot. Stir in the fresh thyme, brown sugar, and balsamic vinegar.

Return the short ribs to the pot, making sure they are submerged in the liquid. Bring to a simmer, then cover the pot and transfer it to the preheated oven.

Braise the short ribs for about 3 hours, or until they are tender and easily fall apart.

While the short ribs are braising, prepare the parsnip gravy. In a medium pot, add the chopped parsnips and cover with water. Bring to a boil and cook until the parsnips are tender, about 15 minutes.

Drain the parsnips and return them to the pot. Add the heavy cream and butter, then mash until smooth. Season with salt and pepper to taste and set aside.

Once the short ribs are done, remove them from the oven and let them rest for a few minutes. Skim any excess fat from the surface of the braising liquid.

To serve, place the short ribs on a plate, drizzle with the pomegranate glaze from the pot, and spoon the velvety parsnip gravy alongside.