For the Short Ribs:

1. Preheat and sear: Preheat oven to 350°F. Liberally season all the short ribs with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Dredge the short ribs in flour and sear on the meaty side for 2 minutes until slightly browned. Place the seared short ribs into a large oven-safe roasting pan with the meaty side facing down and the bone side facing up. Repeat until all short ribs are seared.
2. Make the braising liquid: In a large bowl, whisk together the chicken broth, red wine, Worcestershire sauce, tomato paste, and liquid smoke. Pour this mixture into the roasting pan. If the liquid doesn’t cover the short ribs about halfway, add more chicken broth. Add the beef bouillon cubes, minced garlic, chopped onions, red pepper flakes, and bay leaves. Sprinkle with additional salt and pepper.
3. Braise: Cover the roasting pan with the lid and place in the oven for 2½ hours undisturbed.
4. Add vegetables: After 2½ hours, add the carrots to the pan, cover again, and return to the oven for another 45 minutes.
5. Rest and serve: Remove from the oven and let rest for 15 minutes. The meat should fall off the bone easily—remove and discard the bones. Cover with aluminum foil to keep warm until ready to serve.

For the White Cheddar Mashed Potatoes:

1. Boil the potatoes: Fill a large pot with water and add the potatoes. Bring to a boil over medium-high heat and cook for 25-30 minutes until fork-tender.
2. Mash: Drain the water and return the potatoes to the pot. Use a potato masher to mash the potatoes while still hot. Add the butter and half-and-half, stirring until smooth and creamy.
3. Add cheese: Stir in the white cheddar cheese until melted and fully incorporated. Season with salt and pepper to taste.
4. Serve: Spoon the mashed potatoes onto plates and top with the braised short ribs. Drizzle with the braising liquid from the pan.