Rinse farro (and pick out any rogue pieces that are not farro). Set aside.
Heat the olive oil in a large skillet. Add the onion; cook and stir until the onion is translucent. Stir in the garlic and red pepper flakes. Add the drained farro. Cook, stirring often, until the farro has a nutty smell and is just starting to brown.
Transfer to a large pot, cover and simmer about one hour, until the farro is tender to the bite. Or use a pressure cooker: bring to pressure and cook 20 minutes, then release the pressure by running cold water over the top. Either way, be sure the farro is tender to the tongue—al dente.
While the farro is cooking, blanch the kale, if using; bring a pot of well-salted water to a boil. Add the kale and cook for 5 minutes. Drain and when cool, chop into 1-inch pieces.
When the farro is done, drain, reserving the liquid. Pour about 2 cups of the farro cooking liquid back into the pot along with the farro.
Stir in the cooked white beans, the tomatoes and cooked kale, or parsley leaves. Bring back to a simmer, adding more reserved liquid if needed for a stew-like consistency.
Taste and adjust the seasoning with salt.
Just before serving, drop the mozzarella cubes into the pot.
Ladle into soup bowls. Garnish with parsley leaves, if desired.