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Sprinkle pieces of meat with 1 tablespoon salt (11/2 teaspoons if using table salt), place on wire rack set in rimmed baking sheet, and let stand at room temperature 1 hour.
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2. Adjust oven rack to lower-middle position and heat oven to 300 degrees. Heat butter in heavy-bottomed Dutch oven over medium heat. When foaming subsides, add onions and cook, stirring occasionally, until softened and beginning to brown, 8 to 10 minutes. Add carrot and celery; continue to cook, stirring occasionally, for 5 minutes longer. Add garlic and cook until fragrant, about 30 seconds. Stir in 1 cup broth, 1/2 cup wine, tomato paste, bay leaf, and thyme sprig; bring to simmer.
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3. Pat beef dry with paper towels and season generously with pepper. Using 3 pieces of kitchen twine, tie each piece of meat into loaf shape for even cooking.
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4. Nestle meat on top of vegetables. Cover pot tightly with large piece of foil and cover with lid; transfer pot to oven. Cook beef until fully tender and sharp knife easily slips in and out of meat, 31/2 to 4 hours, turning halfway through cooking.
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5. Transfer roasts to cutting board and tent loosely with foil. Strain liquid through mesh strainer into 4-cup liquid measuring cup. Discard bay leaf and thyme sprig. Transfer vegetables to blender jar. Allow liquid to settle 5 minutes, then skim any fat off surface. Add beef broth as necessary to bring liquid amount to 3 cups. Place liquid in blender with vegetables and blend until smooth, about 2 minutes. Transfer sauce to medium saucepan and bring to simmer over medium heat.
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6. While sauce heats, remove twine from roast and slice against grain into 1/2-inch-thick slices. Transfer meat to large serving platter. Stir chopped thyme, remaining 1/4 cup wine, and vinegar into sauce and season to taste with salt and pepper. Spoon half of sauce over meat; pass remaining sauce separately.
