Heat olive oil in a large enameled cast-iron casserole until shimmering.

Season short ribs with salt and pepper.

Add short ribs to the casserole in a single layer.

Cook over moderately high heat, turning occasionally, until browned (10 minutes).

Transfer short ribs to a plate.

Pour off all but 1 tablespoon of fat from the casserole.

Add onions and a pinch of salt.

Cook over moderate heat, stirring occasionally, until browned (12-15 minutes).

Add tomato paste, garlic, and oregano.

Cook, stirring, until fragrant (2 minutes).

Add crushed tomatoes with their juices and the carrot.

Bring to a boil.

Return short ribs and their juices to the casserole, cover partially, and simmer over low heat.

Turn short ribs occasionally, until the meat is very tender and the sauce is thick (4 hours).

Transfer short ribs to a plate; discard the carrot.

Discard the bones and cut the meat into 1 1/2-inch chunks.

Return the meat to the sauce and season with salt and pepper.

Keep warm over low heat.

Cook spaghetti in a large saucepan of salted boiling water until al dente.

Drain the pasta, reserving 1/2 cup of the cooking water.

Transfer spaghetti to the pot with the sauce.

Toss well and cook for 1-2 minutes.

Add a splash of the reserved pasta water if the sauce is too thick.

Serve the pasta immediately.