How to Make It
In a medium saucepan, combine the beef broth with 1/2 cup of water and bring to a simmer over high heat. Remove from the heat, cover and keep warm.
In a large enameled cast-iron casserole, heat 2 tablespoons of the olive oil. Season the short ribs with salt and pepper. Add half of the short ribs to the casserole, spreading the pieces out, and cook over moderately high heat, turning occasionally, until browned, about 5 minutes. Using a slotted spoon, transfer the browned meat to a plate. Repeat with the remaining short ribs.
Add the remaining 1 tablespoon of olive oil to the casserole. Add the thyme sprigs, garlic, onions, carrot and parsnip and season with salt and pepper. Cook over moderate heat, stirring, until the vegetables are lightly browned, about 5 minutes. Stir in the farro and the browned short ribs. Add the wine and cook until evaporated, stirring and scraping the bottom of the casserole, about 2 minutes. Add 1 cup of the warm broth, cover partially and cook over moderately low heat for 15 minutes, stirring occasionally. Repeat this process twice, adding 1 cup of warm broth each time and cooking for about 15 minutes between additions, stirring occasionally.
Increase the heat to high. Add the remaining 1 cup of warm broth, 1/2 cup at a time and stirring constantly, allowing it to be absorbed before adding more. Cook the farrotto until creamy and the farro is al dente, about 5 minutes longer. Remove the casserole from the heat and discard the thyme sprigs. Stir in the butter, chopped thyme and the 1/4 cup of grated Parmigiano. Season the farrotto with salt and pepper and serve hot, passing additional Parmigiano at the table.