Season the short ribs with salt. Brown them in a pan with some olive oil over medium-high heat. Ensure all sides are browned by turning them as needed to get a good sear. More browning means more flavor.

Once the short ribs have plenty of color, remove them from the pan and set them aside. Add diced onions, celery, and carrots to the pan. Cook them until they have softened and slightly browned, about 10 minutes, stirring occasionally.

After the vegetables have cooked, add tomato paste and cook until it changes from bright red to a brick red color, almost rust-colored. This step cooks the tomato paste. Stir constantly to prevent burning; it should only take a few minutes.

Add wine or water to the pan and scrape off any bits stuck to the bottom.

Return the short ribs to the pan, along with any juices they released. Add thyme and bay leaves, ensuring the short ribs are covered at least 3/4 of the way with liquid. If needed, add more water, and it's fine if the short ribs are fully submerged.

Cover and let the sauce cook. Depending on your cooking method, it may take 40 minutes in a pressure cooker, 3 hours simmering on the stovetop, 6-8 hours in a slow cooker on low, or 3 hours in the oven at 350°F (175°C). You'll know it's cooked long enough when the meat is super tender, easily falls apart, and the bones slide right out.

To finish the sauce, remove the thyme bundle and bay leaves. Remove the short ribs; they should be falling apart. Remove any bones and gently shred the meat. Also, remove any excess bits of fat or connective tissue that hasn't broken down.

Add the shredded meat back into the sauce. If the sauce seems too thin, let it simmer and reduce for a bit. If it's too thick, add a touch of water. Once it reaches your desired consistency, adjust the seasoning if needed, and then serve!

If serving over pasta, you can add a good amount of pasta water to achieve a silky, saucy consistency. Enjoy!