Preheat the oven to 325 degrees. In a Dutch oven, heat olive oil over high heat. Season the ribs with salt and pepper and cook, turning, until browned, 8 to 10 minutes. Transfer to a plate.
Discard all but 2 tablespoons grease. Add the onion and garlic and cook over medium heat for 4 minutes. Slowly add 1 cup water and stir, scraping up any browned bits. Add the coca-cola and ribs. Bring to a simmer, then cover; transfer to the oven and roast until tender, about 3 hours.
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.
Meanwhile, In a saucepan, bring 3 cups water to a boil. Whisk in the polenta and cook, stirring with a wood spoon, for 2 minutes. Remove from heat, stir in the goat cheese. Serve the ribs over the creamy polenta and drizzle with sauce.
Cook’s Note: If you don’t want to serve the ribs on the bone, pull off the cooked meat and pile it on the polenta.