Heat a dutch oven or large skillet to medium high heat. Sprinkle your short ribs with salt and pepper. Once the pot is hot, coat with oil and add the short ribs. Cook for about 3 minutes per side, or until browned. Set the short ribs aside and drain all but 1 tbsp of the grease. Place the ribs in the bottom of the slow cooker.
Add the onion, celery, and carrots to the oil and cook until softened, about 5 minutes. Add the dried basil and rosemary, flour (or arrowroot) and cook another 1-2 minutes.
Deglaze the pan with red wine and broth and stir until the mixture begins to thicken slightly. Add in the tomatoes and tomato paste.
Top the short ribs with the vegetable and red wine in the slow cooker, then add bay leaves. Set the slow cooker to low and cook for 6 to 8 hours.
Remove the beef from the slow cooker, it should be very tender and falling apart. Also remove the bay leaves. You may even see the meat already off the bone. Spoon any additional fat off the top of the sauce if you prefer. See notes below on cooking in advance and refrigerating.
Add salt and pepper to taste. Serve over Instant Pot Mashed Potatoes, or Polenta with fresh thyme (if using)