Preheat the oven to 325 degrees . In a Dutch oven, heat 1 tbsp. EVOO over high. Season the ribs with salt and pepper and cook, turning, until browned, 8 to 10 minutes. Transfer to a plate. Discard all but 2 tbsp. grease. Add the onion and garlic and cook over medium, 4 minutes. Add 1 cup water and stir, scraping up any browned bits. Add the cola and ribs. Bring to a simmer, then cover; transfer to the oven and roast until tender, about 3 hours.
In a skillet, heat the remaining EVOO over medium. Add the kale and 1 cup water; cover and cook, 10 minutes. Uncover and cook over high until pan is dry, 2 minutes. Season. In a saucepan, bring 3 cups water to a boil. Add the polenta and cook, whisking, 2 minutes. Remove from heat, stir in the cheese and season.
Transfer the ribs to a plate. Skim the fat from the sauce and discard; simmer the sauce over medium-high until reduced, 8 to 10 minutes. Stir in the vinegar; season. Serve the ribs with the polenta, sauce and kale.