Season the ribs with salt and pepper. In a large Dutch oven, heat 1 tablespoon of the olive oil over medium-high heat. Add half of the short ribs and brown on each side, about 2 minutes per side. Transfer the caramelized ribs to a plate. Repeat with the remaining 1 tablespoon of olive oil and second batch of the short ribs.
Preheat the oven to 325°. Pour off all but 2 tablespoons of fat from the Dutch oven. Add the apples, onions, carrots and garlic and saute over medium-high heat until softened, about 10 minutes.
Stir in the flour and cook for 1 minute, ensuring the flour gets totally cooked out. Add the stock, wine, coffee, mustard, thyme and bay leaves and bring to a boil. Add the reserved short ribs, cover and braise in the oven until the ribs are tender--you want them falling off the bone--about 2.5-3 hours.
When you're ready to serve, follow the package instructions on the polenta, using 1 cup of the corn grits. Stir in 2 tablespoons of butter.
Arrange the polenta on a large serving platter. Using a slotted spoon, transfer the short ribs on top of the polenta.
Strain the braising liquid through a fine sieve into a heatproof bowl; remove the solids (the carrot and onion mixture) and serve alongside the short ribs. Discard the bay leaves.
Skim the fat off the braising liquid (or you can pour the strained liquid into a gravy fat separator) and pour the sauce over the short ribs and polenta. Garnish with fresh parsley. Enjoy!