Put the pancetta in a large Dutch oven or other heavy pot. Set over medium heat and cook, stirring occasionally, until the fat renders and the meat is golden brown, about 6 minutes. Add the garlic and carrot, reduce the heat to medium-low, and cook, stirring often, until the vegetables are tender, about 3 minutes.
Add the sauce and beans and bring to a simmer. Simmer for 5 minutes.
While the sauce cooks, cook the papparadelle according to the package's directions. Drain well and immediately transfer to the pot with the sauce. Gently toss until evenly coated.
Divide among serving plates and top with the basil. Serve immediately.
You can substitute bacon for the pancetta and tagliatelle for the papparadelle. To make this extra spicy, add a pinch of chile flakes.