Heat oil in a soup pot over medium heat. Add onion and saute until softened, 2-3 minutes. Add garlic and saute 1 minute. Add grain and stir to coat.
Add broth, water, squash, tomatoes, thyme, and salt. Bring to a boil, breaking up the tomatoes and squash with the spoon.
Reduce heat, partially cover and simmer until squash is tender and the grain is cooked (about 30 minutes). Stir in the beans, spinach puree, and kale and simmer 2 minutes, until kale is tender. Stir in cheese and serve hot.