1. Rinse and dry the bell peppers, then place them on a parchment-lined tray. Preheat the oven to 480°F (250°C) and bake the bell peppers, flipping halfway, until the skin is charred and soft and the peppers start to collapse (about 40 minutes, depending on size and oven).

For the Soup

1. Meanwhile, mince the onion and garlic. Sauté in a saucepan with 3 tbsp extra-virgin olive oil over medium heat until smooth and translucent, stirring occasionally. Store the vegetables in a covered bowl.
2. When the bell peppers are fully roasted, place them in sealed ziploc bags, separating reds and yellows. Handle with care; they contain scalding liquid. Wait 15 minutes; the vapors will help remove the skin.
3. Discard the stems and seeds, and eliminate the liquid inside the peppers. Peel the peppers while hot, starting with the yellow ones. Dice the red peppers, salt as needed, and place in a strainer to remove excess liquid.
4. Blend the yellow pepper fillets with 3 tbsp extra-virgin olive oil, Pecorino Romano cheese, and black pepper until smooth.
5. Make this step just before cooking the pasta to maintain crunchiness. Fry pancetta crumbles in a pan over medium heat in their own fat, stirring frequently. When crunchy and golden brown, discard excess fat and place the meat on paper towels.
6. Cook pasta in 5 qt of boiling water with 4.5 tbsp coarse salt. Meanwhile, heat the yellow pepper sauce in a pan with coarsely chopped basil over medium-low heat, salting as needed. When pasta is al dente, toss with the sauce, pancetta crumbles, and diced red peppers. Serve immediately.