Preheat the oven to 325°F (160°C).

Season the beef short ribs with salt and pepper. In a large Dutch oven or heavy pot, heat the olive oil over medium-high heat. Add the short ribs in batches, browning them on all sides. Remove the ribs and set aside.

In the same pot, add the diced onion and cook until soft, about 5 minutes. Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.

Add the chopped dried plums to the pot, along with the beef broth, red wine, tomato paste, rosemary, and thyme. Stir to combine and bring to a simmer.

Return the browned short ribs to the pot, ensuring they are submerged in the liquid. Cover the pot with a lid and transfer it to the preheated oven. Braise for 3 hours, or until the beef is tender and falling off the bone.

While the ribs are cooking, prepare the roasted root vegetables. Toss the chopped carrots and parsnips with olive oil, salt, and pepper. Spread them out on a baking sheet and roast in the oven for about 30-40 minutes, or until tender and caramelized.

Once the short ribs are done, remove them from the pot and set aside. Strain the cooking liquid into a saucepan, discarding solids.

In the saucepan with the strained liquid, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes. Gradually add the strained liquid, whisking continuously until the gravy thickens. Adjust seasoning with salt and pepper.

To serve, place the short ribs on a plate, drizzle with the silky gravy, and add a generous serving of roasted root vegetables on the side.