Place a deep skillet or braising dish on stove. Add oil and then set heat to high. While it heats up, pat dry your short ribs and season with salt and pepper.
Once the oil is hot, add short ribs and begin to sear until a deep brown crust forms, about 2-3 minutes. Do not crowd the pan. I could only fit 3 ribs in my pan at once so I did this in batches. Flip 90 degrees and continue browning all the sides. Turn off heat. Place short ribs in the bottom of a slow cooker, rib-side down. Do not turn on slow cooker yet.
Pour any juice out of the skillet/braising dish. Place back on heat and set to medium. Add minced shallots and diced celery. Cook until tender, about 5 minutes. Add tomato paste and push into the veggies using the back of the wooden spoon. Cook for another 3-4 minutes.
Slowly pour the beef broth into the pan. Carefully, it may sizzle violently at first. Add red wine and stir together. Whisk in the flour, making sure to remove most of the lumps, Add bay leaves, fresh thyme, salt, and pepper. When adding salt and pepper, taste first and then gradually add so you don't over-season. I start with 1/4 teaspoon at a time.
Bring sauce to a boil and then reduce to a simmer. It will probably be steaming. Turn off heat and pour sauce over the short ribs. Try your hardest to get the short ribs as submerged in the liquid as you can. Cook for 7-8 hours on HIGH or 11-12 hours on LOW. You'll know it's ready when it begins fall apart with only your fork. All the bones fell out of my short ribs, too.
Serve with chunky mashed potatoes or hearty noodles, like pappardelle.