How to Make It
Bring a large saucepan of water to a boil. Add the farro, rosemary, garlic, a generous pinch of salt and 2 tablespoons of the olive oil and simmer over moderate heat until the farro is tender, 20 to 25 minutes. Drain the farro and spread on a baking sheet to cool; discard the rosemary and garlic.
In a large skillet, heat the remaining 1/3 cup of olive oil until shimmering. Add the sausage and cook over moderate heat, breaking the meat into pieces, until it starts to brown, about 4 minutes. Add the shiitake and cook, stirring, until just tender, about 3 minutes. Stir in the farro, radishes and scallions and cook, stirring, until the farro is coated and the radishes are crisp-tender, about 5 minutes. Remove from the heat. Stir in the parsley and season with salt and pepper; keep warm.
Fill a large, deep skillet with water and bring just to a simmer. One at a time, crack the eggs into the simmering water. Poach the eggs until the whites are set and the yolks are runny, about 4 minutes. Using a slotted spoon, transfer the eggs to a paper towel–lined plate and season with salt and pepper. To serve, spoon the sausage fried farro into shallow bowls and top with the eggs.