Heat 3 tablespoons of the olive oil in a large saute pan over medium heat. Add the cabbage and saute until wilted but still a little firm, about 5 minutes. Transfer to a bowl.
To the same pan, add 1/4 cup of the olive oil. Add the rosemary sprigs and cook for 4 minutes over medium heat, turning every minute, until the rosemary leaves get crisp and lightly browned. Remove to a paper-towel-lined plate to drain.
Add the fusilli to the pan and toast until the edges are browned, 3 to 4 minutes. Add the toasted pasta to the pot of boiling water and cook until al dente, 8 to 10 minutes.
Meanwhile, heat the remaining 3 tablespoons olive oil in the saute pan over medium heat. Add the onions and saute until translucent, about 3 minutes. Add the garlic and saute 1 minute more. Add the cannellini beans, red pepper flakes, and a generous pinch of salt and pepper; saute for another 2 minutes. Add the vegetable broth, butter and lemon juice. Turn the heat down to low and simmer for 3 minutes.
Drain the pasta and add it to the saute pan. Raise the heat to medium, give the pasta a good stir, and cook for 1 minute. Stir in the sauteed cabbage. Crumble the fried rosemary with your hands and stir it into the pasta. Taste and adjust the seasoning with salt and pepper as needed. Serve immediately.