Sprinkle the roast all over with 2 1/2 teaspoons salt and 1 1/2 teaspoons pepper. Coat in flour and shake off any excess. Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high heat. Add the roast to the skillet and cook until golden brown on all sides, about 8 minutes, turning as needed. Transfer the roast to the insert of a 6-quart slow cooker, along with the carrots, celery, onions and garlic.
Add the remaining 1 tablespoon oil to the skillet over medium heat. Add the tomato paste and stir until the oil begins to turn brick-red, about 1 minute. Add the flour and wine and whisk until thick (it's OK if there are some lumps). Add the beef broth, bay leaves, thyme, allspice, 1/2 teaspoon salt and a few grinds of pepper and bring to a simmer, whisking, until the gravy is smooth and thickens slightly, about 4 minutes.
Pour the gravy into the slow cooker. Cover and cook on low for 8 hours. The roast and vegetables should be tender.
Remove the roast and let rest for a few minutes. Discard the thyme stems and strain the vegetables, reserving the gravy. Toss the vegetables with half the parsley and season with salt and pepper. Stir the remaining parsley into the gravy and season with salt and pepper. Slice the roast against the grain. Serve the meat and vegetables on a platter, moistening them with some of the gravy; serve the remaining gravy on the side.
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