In a large pot of boiling, salted water, add the farro and cook at a gentle simmer until tender, about 20 minutes. Reserve 4 cups of the cooking water, then drain the farro in a colander.
Meanwhile, in a large dutch oven or soup pot, heat 1/4 cup EVOO and the garlic over medium-low heat until the garlic is softened, about 3 minutes. With a wooden spoon, press down on the garlic to release its flavor; do not brown. Add the carrots and onion and cook, stirring frequently, until softened, about 7 minutes. Stir in the kale and 1/4 cup water, cover the pot and cook until wilted, about 10 minutes. Stir in the cannellini beans and their liquid, the diced tomatoes and their juices, the parsley and crushed red pepper. Lower the heat, cover partially and gently simmer for 10 minutes.
Add the drained farro and 3 cups of the reserved cooking water to the soup; add the final cup of cooking water if desired to thin the soup. Season with salt and pepper. Simmer for 10 minutes over medium heat. Ladle into bowls and drizzle about 1 tbsp. EVOO over each serving.