Char the skins of the 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 off the top 1/4 of the head garlic to expose the cloves, drizzle on 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 40-45 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. Roast until very tender, 30-40 minutes. Cool the eggplant until it's 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; puree.
In a saucepan, heat the stock and tomatoes. If the tomatoes are whole, break them up with a potato masher or fork. Stir in the eggplant/pepper mixture. 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 the grated Pecorino cheese and a sprinkle fresh parsley on top. With a nice green salad and some rustic bread, you've got a great meal!