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Step 1
Dice 1 large yellow onion, peel and cut 2 medium carrots into 1-inch pieces, and cut 2 celery stalks into 1-inch pieces.
Step 2
Pat 3 to 3 1/4 pounds short ribs dry. Season all over with 2 teaspoons of the kosher salt and 1/2 teaspoon black pepper. Heat 1 tablespoon of the vegetable oil in a large, high-sided frying pan or Dutch oven over medium-high heat until shimmering. Add half of the short ribs and sear on 3 sides, 3 to 4 minutes per side.
Step 3
Transfer with tongs to a 6-quart or larger slow cooker. If needed, add the remaining 1 tablespoon vegetable oil and repeat with the remaining short ribs. Transfer with tongs to the slow cooker. The short ribs will not be cooked through. Add 1 cup low-sodium beef broth, 4 fresh sprigs thyme, and 2 bay leaves to the slow cooker.
Step 4
Add the onion, carrot, and celery, to the pot, season with the remaining 1 teaspoon kosher salt, and cook, stirring occasionally until softened, about 5 minutes. Add 1/4 cup all-purpose flour and 2 tablespoons tomato paste, stir to coat the vegetables and cook until darkened in color, about 2 minutes. Pour in 3 cups dry red wine and stir to combine, scraping up any browned bits. Bring to a boil. Reduce the heat and simmer until slightly thickened, about 5 minutes.
Step 5
Pour the hot liquid and vegetables into the slow cooker. Cover and cook on the LOW setting until the meat is tender and pulls away from the bone, 8 to 10 hours.
Step 6
Transfer the short ribs to a large plate with tongs. Some of the short ribs may separate from the bone. Strain the liquid through a fine-mesh strainer into a large glass measuring cup or bowl and discard the cooked vegetables, bay leaves, thyme sprigs, and any loose bones. Serve the short ribs with sauce spooned over top.