In a heavy-bottomed pan like a Dutch oven, combine the white beans, sage, garlic, 2 tablespoons olive oil, parmesan rind, and 6 cups water.
Bring to a boil over medium-high heat. Reduce the heat to medium-low to maintain a gentle simmer.
Cook, partially covered, for 1 hour 20 minutes, stirring occasionally; the beans should be just tender all the way through.
Remove sprig of sage and any leaves that many have come off the stem during cooking and the parmesan rind.
Add the kale, salt, and red pepper flakes to the beans and stir to combine. Cover the pan and simmer until the kale is wilted, an additional 15 minutes. Stir in the remaining 1/4 cup olive oil and the grated parmesan cheese to finish.