Soak beans in a bowl with water to cover at least 4 hours (at least 6 hours if using Corona) or overnight. Drain, put in a 5- to 6-qt. pot, and add 2 qts. broth, 6 garlic cloves, the sage, and 1/4 tsp. chile flakes. Bring to a boil, then reduce heat and simmer until tender, 40 to 80 minutes, adding 1/2 tsp. salt during last 15 minutes.
Fill another large pot about three-quarters full of water and bring to a boil over high heat. Submerge kale and boil gently until tender, 10 to 15 minutes. Drain, then coarsely chop.
Heat 1/3 cup oil over medium heat in pot used for kale. Chop remaining 4 garlic cloves and add to pot with remaining 1/4 tsp. chile flakes and the rosemary; sauté until garlic is fragrant, about 2 minutes. Add anchovies and kale and cook a few more minutes. Stir in beans and their liquid. Cover and bring to a boil, then reduce heat and simmer 10 minutes. Remove from heat.
Stir bread into soup with pepper and salt to taste. Cover and let stand until bread is very soft, 20 minutes to 1 hour.
Reheat soup over medium heat until steaming, adding more broth if you'd like a looser texture. Ladle into bowls and add pecorino and a drizzle of oil.
*Get Corona beans (large, plump white beans) from purcellmountainfarms.com
Note: Nutritional analysis is per serving.