Season the short ribs generously with the flour, salt and pepper. Heat a large Dutch oven or heavy-bottomed pot over high heat and add the oil. Add the short ribs in batches and brown on all sides, about 3 minutes per side. Transfer the ribs to a plate.
Meanwhile, add the carrots, celery and onion to a food processor and pulse until the vegetables are almost a puree, about 30 seconds.
Reduce the heat under the pot to medium high, add the vegetable puree and saute, stirring often, until the veggies are softened, about 5 minutes. Add the tomato paste, Italian seasoning and a pinch of flour. Cook, stirring constantly, until the tomato paste darkens slightly, about 3 minutes. Slowly pour in the wine while whisking; whisk until smooth and combined. Add the sugar to the wine. Bring to a boil, reduce to a simmer and cook until the wine is reduced by half, 10 to 15 minutes.
Stir in the broth, garlic and bay leaves, bring to a boil, turn off the heat and add the ribs back to the pot. Cover, transfer to the oven and cook until the ribs are tender, about 3 hours. Serve over sweet potato polenta.