Preheat the oven to 325°F (165°C).
In a large ovenproof pot or Dutch oven, heat olive oil over medium-high heat. Add short ribs and brown on all sides, about 10 minutes.
Remove the ribs from the pot and set aside. In the same pot, add garlic and sauté until fragrant.
Add pomegranate juice, brown sugar, balsamic vinegar, salt, and pepper. Stir to combine and bring to a simmer.
Return the short ribs to the pot, ensuring they are mostly submerged in the liquid.
Cover the pot and transfer it to the preheated oven. Cook for 3 to 3.5 hours, until the short ribs are tender and the sauce has thickened.
Remove from oven, let rest for a few minutes, and serve warm. Decorate with pomegranate seeds.