Preheat the oven to 400°F. Rub the peppers all over with a little olive oil and place them on a baking sheet, leaving a space between each pepper. Roast the peppers, turning them every 15 minutes or so, until they are well charred and blistered on all sides and beginning to collapse, about 30 to 40 minutes.

Remove the baking sheet from the oven and immediately place the peppers in a bowl and cover it tightly with aluminum foil to trap in the vapors while the peppers are emitting their steam. Set aside for about 15 minutes, or until their skins have loosened and they are cool enough to handle.

Remove the skin with a sharp knife and trim off the stem. Pour any of the peppers remaining juices into a small bowl, then split the peppers open and lay them out flat on a work surface. Scrape away the seeds and inner membranes, then cut the peppers into 1-to 1 1/2-inch thin strips. Set the peppers aside in the bowl with their juices.

Slowly bring a large pot of water to a rolling boil.

Meanwhile, in a 12-to 14-inch sauté pan over medium-low heat, combine the olive oil and onion and gently sauté until the onion has softened, about 3 to 4 minutes, stirring occasionally. Add the garlic, rosemary, and pepper flakes and stir just until the garlic is fragrant, about 30 seconds. Add the sausage and oregano and stir occasionally until the meat is lightly browned with no pink remaining, about 5 to 6 minutes.

Pour in the wine and bring to a boil. Reduce the heat slightly and simmer until the wine is almost fully absorbed. Stir in the tomatoes and season with salt and a few grindings of black pepper. Partially cover the pan and cook, stirring occasionally, for 15 to 20 minutes or until the tomatoes break down and release their juices.

Add the roasted peppers and their juices to the pan and stir for a couple of minutes longer just to blend the flavors. Taste for seasoning and add more salt and pepper, if necessary. Reduce the heat to low and leave the sauce very gently simmering on the stove while you cook the pasta.

Salt the boiling water and drop in the pasta. Stir to separate the strands. Return the water to a boil and cook until the pasta is just under al dente, tender but firm to the bite, about 2 to 2 1/2 minutes. Drain the pasta in a colander, reserving 1 cup of the pasta cooking water.

Add the pasta, Parmigiano, and basil to the saucepan and gently toss for about 2 minutes or until the pasta is al dente and well coated with the sauce, adding a little more pasta cooking water, if more liquid is needed.

Divide the pasta among the plates and serve immediately sprinkled with Parmigiano and garnished with basil.