Heat the olive oil in a medium saucepan set over medium heat.
Add the farro and cook, stirring occasionally until the grains are coated and you begin to hear a popping sound sound. Stir in the onion and cook until translucent, about 4 minutes.
Add the broth and bring to a boil. Lower the heat and simmer until the liquid is absorbed and the farro is cooked through but al dente, about 12 more minutes.
Transfer the farro to a bowl let it cool about 5 minutes.
Add the Parmesan cheese, sun-dried tomatoes, parsley and the eggs.
Mix well and season with salt and pepper to taste. Set aside about 15 minutes.Meanwhile heat about ¼-inch vegetable oil in a large non-stick or cast iron skillet set over medium-high heat until quite hot, but not yet smoking. Using a large spoon, drop batter in 2-tablespoonful mounds into oil. With a small spatula or butter knife, gently flatten each mound and fry until golden, about 4 minutes per side, carefully flipping once (adjust heat if browning too quickly).
Drain on paper towels. Season with more salt and serve warm.