Sprinkle beef all over with the salt.

Heat 1 tablespoon of the oil in a Dutch oven over medium-high heat until shimmering. Add two of the shanks and cook until browned underneath, about 4 minutes. Flip and brown the other side, about another 4 minutes. Transfer to a plate. Add the remaining tablespoon of oil and brown both sides of the other two shanks, and then transfer them to the plate as well.

To the Dutch oven add the onion, carrot, and celery. Reduce heat to medium and cook, stirring occasionally, until just starting to brown in spots, about 4-5 minutes.

Add the garlic and stir and cook for 30 seconds and then pour in the wine. Stir and scrape up any browned bits from the bottom of the pot. Add the diced tomatoes, 1 cup of the broth, and the thyme. Stir.

Add the beef shanks back in, overlapping them so that they are mostly submerged. Increase heat to high and bring to a boil. Reduce heat to low.

Partially cover the pot and allow to simmer, stirring occasionally, until beef is very tender and pulls away from the bone, about 1.5 hours. (Alternatively, put the lid on and put the Dutch oven into the oven at 300°F for 1.5 hours, no need to stir).

Transfer beef to a serving platter. Skim fat off of liquid in Dutch oven, if desired.

Measure the flour and the remaining ½ cup of beef broth into a mason jar or container with tight-fitting lid. Shake it until no lumps remain. Stir it into the liquid in the Dutch oven. Cook over medium-high heat, stirring frequently, until sauce thickens, about 3-4 minutes.

Taste and add more salt, if desired. Serve meat topped with sauce and veggies.