Prepare pasta according to package directions, omitting salt. Reserve 1/4 cup of pasta water and drain.
Meanwhile, heat oil in large skillet over medium heat. Cook onion and carrot 6 minutes, stirring, or until onion softens and begins to brown. Stir in garlic and red-pepper flakes. Cook 1 minute, stirring, or until fragrant.
Add half greens and 1/2 cup water. Increase heat to medium-high, cover, and cook for 2 minutes, or until greens wilt. Stir in remaining greens. Reduce heat to medium, cover, and cook 10 minutes, or until greens are tender. Stir in beans. Cover and cook 2 minutes, until beans are hot.
Stir in pasta and reserved pasta cooking water. Cook 2 minutes, stirring, or until pasta is hot. Remove skillet from heat and stir in 2 Tbsp of the cheese. Serve sprinkled with remaining 1 Tbsp cheese.