Char the skins of sweet and hot peppers to black under a broiler with oven door slightly ajar, to prevent steam build up or place directly over stovetop flame. Cover the charred peppers and cool, peel, and seed. Reserve.
Preheat the oven to 425 degrees F.
Cut head garlic to expose the cloves, dress in extra-virgin olive oil and season with salt and pepper. Press the garlic into the chopped rosemary and coat the cut cloves. Wrap the garlic up in foil and roast 40 to 45 minutes, until soft but still moist.
Halve the eggplant lengthwise and brush with extra-virgin olive oil. Season the eggplant with salt and pepper and place cut-side down on baking sheet and roast to very tender, 30 to 40 minutes. Cool the eggplant until easy to handle, then scoop the flesh away from skins and add to a food processor with roasted garlic and roasted sweet and hot peppers, then puree.
In saucepan, heat the stock and tomatoes. If the tomatoes are whole, break them up. Stir in the eggplant-pepper mixture and add basil and oregano, salt, and pepper, to taste.
Simmer sauce to combine flavors then cool and store for make-ahead meal.
Reheat over medium heat.
Boil long, curly pasta in salted water to al dente, toss the pasta with sauce and serve with cheese and a sprinkle fresh parsley.