Preheat the oven:
Preheat your oven to 350°F (175°C).

Sear the short ribs:
Season the short ribs with salt and pepper.
Heat olive oil in a large, oven-safe pot (Dutch oven works well) over medium-high heat.
Add the short ribs and sear on all sides until they are browned (about 3-4 minutes per side). Remove from the pot and set aside.

Sauté the vegetables:
In the same pot, add the chopped onion, carrots, and celery. Sauté for about 5-7 minutes until softened.
Add the garlic and cook for another minute until fragrant.

Deglaze the pot:
Add the red wine (or more beef broth if not using wine), scraping the bottom of the pot to loosen any browned bits.
Stir in the tomato paste and thyme, mixing well.

Braised short ribs:
Return the short ribs to the pot, and pour in the beef broth, covering the ribs halfway.
Bring to a simmer, then cover with a lid and transfer to the oven.
Braise for 2.5-3 hours, until the meat is tender and falling off the bone.

Prepare the rice:
While the ribs are braising, cook the rice according to package instructions.
Finish and serve:

Once the short ribs are done, remove them from the pot and set them aside.
Skim off any excess fat from the sauce.
Serve the short ribs on a bed of rice, spooning some of the rich sauce and vegetables over the top.
Garnish with fresh parsley.