In a large skillet, heat the olive oil over medium heat. Add the onion and 1 teaspoon salt and cook, stirring occasionally, until softened, about 5 minutes. Add the bell peppers and cook for 5 minutes more. Add 1/2 cup water, lower the heat to medium-low, cover and cook until tender, about 25 minutes.
Meanwhile, in a large pot of boiling, salted water, cook the pasta according to package directions until al dente; drain, reserving 1 cup pasta cooking water. Return the pasta to the pot.
Using a food processor, puree one-third of the bell pepper mixture. Strain through a sieve over the pasta and stir in 1/4 cup parmesan, the butter, cayenne, 1/2 cup pasta cooking water and the lemon juice; add more pasta cooking water to loosen, if necessary. Stir the basil into the remaining bell pepper mixture in the skillet. Divide the pasta among 4 plates, mound the bell pepper-basil mixture on top and sprinkle with the remaining 1/4 cup parmesan.