Heat 1 tablespoon oil in Dutch oven over medium-high heat until just smoking.
Add sausage and cook until lightly browned all over, 5 to 7 minutes.
Add onion and beans and cook, stirring occasionally, until onion is lightly browned, about 5 minutes.
Stir in garlic, fennel seeds, oregano, and pepper flakes and cook until fragrant, about 30 seconds.
Stir in broth and water and bring to boil.
Stir in orecchiette and half of kale.
Cover, reduce heat to medium, and simmer for 4 minutes.
Without stirring, place remaining kale on top of orecchiette.
Cover and continue to cook until kale is just tender, about 4 minutes longer.
Stir to incorporate kale into orecchiette.
Simmer, uncovered and stirring occasionally, until most liquid is absorbed and orecchiette is al dente, 3 to 6 minutes.
Off heat, stir in Pecorino and remaining 1 tablespoon oil.
Season with salt and pepper to taste.
Serve with extra Pecorino.
