How to Make It
Heat oil in a large pot or Dutch oven over medium-high. Add onion, carrots, celery, garlic, and tomato paste. Cook, stirring occasionally, until tomato paste has darkened and vegetables are just tender, about 10 minutes. Stir in broth, beans, tomatoes with juices, farro, and rosemary; bring to a boil. Reduce heat to medium and simmer, stirring occasionally, until farro is tender, about 30 minutes. Stir in up to 3 cups water if soup is too thick. Season with salt and pepper.
Meanwhile, sprinkle cheese in an even layer in a medium nonstick skillet to form a large round. Cook, without stirring, over medium, until melted and browned, about 3 minutes. Remove from heat and let cool in skillet for 3 minutes. Transfer to a plate and let cool briefly; break into pieces.
Stir kale into soup and cook until just wilted, about 5 minutes. Garnish each serving with Parmesan crisps and drizzle with pesto, if using.