In a large saucepan, melt 3 tablespoons of the butter. Add the scallions and cook over moderate heat until softened, about 2 minutes. Add the farro, season with salt and pepper and cook for 1 minute, stirring. Add 1/2 cup of the stock and cook over moderate heat, stirring, until absorbed. Continue adding the stock 1/2 cup at a time, stirring frequently until it is absorbed before adding more. The farro is done when it's al dente, about 30 minutes.
In a medium skillet, heat the olive oil. Add the cauliflower, season with salt and pepper and cook over high heat until tender and browned in spots, about 5 minutes. Add the cauliflower to the farro along with the vinegar and the remaining 2 tablespoons of butter. Season with salt and keep warm.
Bring a saucepan of water to a boil. Add the eggs and cook for 4 minutes. Drain and rinse under cold water. Spoon the farro into 8 bowls. Peel the eggs and carefully remove the egg whites to keep the yolks whole. Carefully place the intact yolks in the center of each bowl of farro; discard the whites. Serve right away.