Pat the short ribs dry and season all over with 2 teaspoons salt and the pepper.
Heat the olive oil in a large Dutch oven over medium-high heat. Sear the short ribs on all sides until deeply browned, working in batches if needed. Transfer to a plate.
Reduce the heat to medium-low. Add the onion, carrots, and celery and cook for 10 to 12 minutes, stirring often, until very soft. Add the garlic and cook for 30 seconds, then stir in the tomato paste and cook for another 2 minutes.
Preheat the oven to 300°F. Pour in the red wine and scrape up the browned bits from the bottom of the pot. Simmer for about 5 minutes, until reduced by about half. Add the whole tomatoes and their juices, breaking the tomatoes up with a wooden spoon. Simmer for about 10 minutes. Taste the sauce and add salt as needed. Return the short ribs to the pot and add the thyme, rosemary, and bay leaf. Cover and braise in the oven for 3 to 3 1/2 hours, or until the beef is very tender and pulls easily away from the bones.
Transfer the short ribs to a cutting board. Remove and discard the bones, cartilage, herbs, and any large pieces of fat. Shred the beef into small pieces and spoon off any excess fat from the surface of the sauce.
Return the shredded beef to the Dutch oven and simmer uncovered over medium-low heat until the ragù is thick and spoonable. It should be thick enough to stay between the layers of lasagna, but not dry. If it becomes too thick, stir in about 1 cup of beef broth to loosen it, then continue simmering until you reach the right consistency again. Add more broth only if needed. Taste and add more salt as needed.