Heat the olive oil in a large Dutch oven over medium-high heat. Add the pork cubes and cook until browned on all sides, about 6 to 8 minutes. Remove the pork and set it aside.
Lower the heat to medium. Add the diced onion to the same pot and cook until softened, about 4 minutes. Stir in the garlic, rosemary, and oregano and cook for 1 minute more.
Pour in the crushed tomatoes and return the browned pork to the pot. Season with salt and black pepper. Bring the mixture to a simmer, then reduce the heat to low, cover, and cook for 45 minutes.
Stir in the white beans and chopped kale. Continue cooking uncovered for 10 to 15 minutes until the kale wilts and the beans are heated through. Taste and adjust seasoning if needed before serving.