Heat some cooking fat in a large skillet placed over a medium-high heat.
Brown the short ribs on all sides, about 2 to 3 minutes per sides. Transfer the short ribs to a slow cooker.
Add onions, carrots, celery, and garlic to the skillet and cook over a medium-high heat, stirring often, until the onions are browned, about 8 minutes.
Add the tapioca starch and tomato paste to the skillet. Cook, stirring constantly, for 2 to 3 minutes.
Stir in the wine, and bring to a boil; then lower the heat to medium and let it simmer for 6 to 8 minutes.
Add the thyme, rosemary, and bay leaf, stir in the beef stock, and stir until well combined.
Pour the sauce over the short ribs and cook on low for 6 to 8 hours.