Season the beef short ribs generously with salt and black pepper on all sides.
Heat olive oil in a large skillet over medium-high heat and sear the ribs until deeply browned on all sides, then transfer them to the slow cooker insert.
In the same skillet, add the onion, carrots, and celery; sauté for 5 minutes until the vegetables begin to soften.
Add the minced garlic and tomato paste to the skillet, cooking for 1 minute until fragrant.
Pour the red wine into the skillet to deglaze, scraping the bottom of the pan to release the browned bits (fond), and let simmer for 2 minutes.
Pour the vegetable and wine mixture over the ribs in the slow cooker.
Add the beef broth, thyme sprigs, rosemary sprigs, and bay leaf to the slow cooker.
Cover and cook on Low for 8 hours (or High for 4 to 5 hours) until the meat is tender and falling off the bone.
Carefully remove the ribs and discard the herb sprigs and bay leaf.
Skim any excess fat from the surface of the cooking liquid and serve the ribs with the sauce over mashed potatoes or polenta.