How to Make It
In a large saucepan, heat the 1/4 cup of olive oil. Add the crushed garlic and the onion and cook over moderately low heat until softened, about 5 minutes. Drain the farro and chickpeas; add them to the saucepan along with the chile and cover generously with water. Bring to a simmer, cover and cook over low heat, skimming occasionally, until the chickpeas are almost tender, about 1 1/2 hours. Uncover and continue simmering until completely tender, about 20 minutes longer. Remove from the heat.
Meanwhile, drain the borlotti beans. In a medium saucepan, generously cover the beans with water and bring to a simmer. Cover and cook until tender, about 2 hours. Transfer 2 cups of the cooked beans to a bowl and mash to a coarse puree. Return the mashed beans to the saucepan.
Drain the chickpeas and farro and return them to the large saucepan; discard the chile. Add the borlotti beans with their liquid and the minced garlic to the saucepan and bring to a simmer. Season with salt and pepper and stir well. Serve the soup hot in bowls. Pass the olive oil and the cheese at the table.