Position a rack in the oven 6 inches below the broiler and preheat the broiler.
Put the peppers on a baking sheet and put it under the broiler. Roast, turning the peppers with tongs a quarter turn every couple of minutes, until charred on all sides, 8 to 10 minutes total. Transfer the peppers to a bowl, cover tightly with plastic wrap, and let the peppers steam for 10 minutes to loosen the skins.
Using a paper towel, rub the charred skins off the peppers. Carefully remove the cores, stems, and seeds, and slice the pieces lengthwise into thin strips. Reserve any liquid the peppers release.
Bring a medium pot of water to a boil and salt it generously. Add the asparagus and cook for 1 minute; drain and rinse under cold water. Transfer to a paper towel-lined plate to drain.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon, until browned and cooked through, 6 to 8 minutes. Transfer the sausage to a plate with a slotted spoon.
Meanwhile, bring a large pot of water to a boil and salt it generously. Cook the pasta until al dente according to the package instructions. Drain and return the pasta to the warm pot.
Add 3 tablespoons olive oil to the skillet, add the eggplant, season with salt and pepper, and cook until brown and just tender, 5 to 6 minutes.
Add 1 tablespoon of olive oil and the garlic to the skillet and cook, stirring, for 1 minute. Add the roasted peppers with any reserved liquid, asparagus, sausage, and vinegar and cook, stirring, for 2 minutes more.
Transfer the sausage mixture to the warm rigatoni and add the Parmesan, parsley, and remaining 2 tablespoons of olive oil and stir to combine.
Taste the pasta and season with salt and pepper, if needed. Transfer to a large bowl and serve immediately.