Heat olive oil in the skillet over medium heat. Salt and pepper the short ribs. Add 2 or 3 ribs and sear each side until browned. Repeat until all ribs are seared, then move them to the slow cooker.
Add the mushrooms to the skillet, cook until browned, and then transfer to the slow cooker.
Add the scallions, sweet onion, garlic, and thyme to the slow cooker.
Mix the pomegranate juice and beef stock. Add the brown sugar and stir to mix well. Pour over the short ribs.
Cook on high for 4-6 hours or low for 6-8 hours or until the ribs are fork-tender.
Sprinkle with pomegranate seeds before serving.
Notes
Skimming Fat
You can skim rendered fat off short ribs by using a fat separator cup.