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Preheat the oven to 350 degrees F.
In a large bowl, add the garlic, carrots, celery, onions, tomatoes, tomato paste, stock and red wine. Stir to combine, then set aside.
Heat a large skillet over medium-high heat. Add the olive oil, and when it begins to shimmer, add the short ribs and cook until golden brown on both sides, 6 to 8 minutes per side. Continue with remaining short ribs until all are browned. Lay the short ribs down on the bottom of the pan.
Pour the tomato and red wine mixture over the short ribs. Cover the pan with a lid and bake until fork tender, 2 to 2 hours 30 minutes.