Preheat the oven to 350°F (175°C).
Heat the olive oil in a Dutch oven or an oven-safe pot with a lid over medium-high heat. Once the oil is hot, sear the boneless short ribs until they're deeply browned on all sides. Transfer them to a plate and set aside.
Reduce the oil in the pot, leaving just a thin layer. Add the diced carrots and onions and sauté over medium heat, stirring often, until the onions turn translucent and begin to soften—about 5 minutes.
Stir in the flour and tomato paste, mixing thoroughly to form a thick base. Let it cook for 1 minute, stirring constantly to prevent scorching.
Pour in the red wine and bring the mixture to a gentle boil. Reduce the heat to medium-low and let the wine simmer until it reduces by half—this should take around 20 to 25 minutes. Take your time with this step to build deep, concentrated flavor.
Once reduced, stir in the broth along with the parsley, thyme, rosemary, and bay leaf. Return the seared short ribs to the pot, nestling them into the liquid. Cover with the lid and place the pot in the preheated oven.
Let the short ribs braise for 1 hour and 15 minutes. Afterward, carefully remove the pot from the oven and add the halved potatoes and carrot pieces. If the braising liquid looks low, add a splash more broth or wine to ensure the vegetables cook properly. Cover and return the pot to the oven for another 1 hour and 15 minutes, or until the meat is fork-tender and the vegetables are soft.
Once done, take the pot out of the oven. Discard all herb sprigs and the bay leaf. Taste the braising liquid and adjust with salt and pepper as needed.
Transfer the short ribs and vegetables to a platter. Allow the sauce to sit undisturbed for 10 to 15 minutes so the fat can rise to the surface. Skim off the excess fat with a spoon.
Return the ribs and vegetables to the pot and warm gently over the stove before serving. Serve hot, spooning the rich, glossy sauce over the top.