Process 1 can of beans and water in food processor until smooth, about 30 seconds. Set aside.
Heat oil in large saucepan over medium heat until shimmering. Add onions, carrots, celery, pancetta, salt and pepper and cook until vegetables are softened, about 10 minutes.
Add tomato paste, garlic and pepper flakes, and cook until fragrant, about 2 minutes. Stir in broth, remaining can of beans and pureed bean mixture. Bring to boil, reduce heat to medium-low, and simmer, stirring occasionally, until flavors have melded, about 10 minutes.
Increase heat to medium and bring to boil. Add pasta and cook, stirring occasionally, until pasta is al dente, about 12 minutes. Off heat, stir in Parmesan and basil. Serve, drizzled with extra oil and passing extra Parmesan separately.