Pat the short ribs dry with paper towels, and season with salt and pepper. Let your short ribs come to room temperature.
In a large Dutch oven or heavy-bottomed pot, heat neutral oil over medium-high heat. Sear your short ribs on all sides until darkened and deeply browned, about 3 to 4 minutes per side.
Add in your onions and garlic and give everything a big toss; season with salt and pepper. Saute until softened, about 3 to 4 minutes.
Pour in the balsamic vinegar and pomegranate juice, scraping up any browned bits from the bottom of the pot. Then, add in your broth. Bring this to a gentle simmer, then bring the heat to low, and cover the pot with a lid.
Keep covered and let your short ribs braise for 4 hours, until fork-tender.
You can serve as is, or make a sauce: Remove the completed short ribs from the pot and set aside, covered with foil to keep warm. Strain the braising liquid from the braise into a fine mesh sieve, discarding any solids.
In a saucepan, make your roux with butter and flour, and slowly add in about 2 cups of your strained broth. Bring the strained liquid to a boil over medium-high heat, and then to a gentle simmer. It should reach a thicker, silky consistency. Season with salt and pepper, as needed.
Plate the short ribs, drizzling over your sauce and pomegranate arils.
Notes
Bone-in Short Ribs: You can use boneless short ribs for this recipe if you prefer!