Trim ends of eggplant; peel, leaving stripes of skin intact. Cut eggplant in half lengthwise and slice crosswise into 1/4-inch slices. Transfer to a large bowl. Add sliced zucchini to bowl. Toss eggplant and zucchini with 2 tablespoons kosher salt and let sit until water begins to release, about 15 minutes.
Whisk olive oil, garlic, chili flakes, and dried oregano together in a bowl.
Rinse salt from veggies in a colander with fresh water. Set aside to drain well.
Place vinegar and water into a saucepan. Bring to a boil over high heat. Place drained vegetables into pan. Cook covered until softened and translucent, about 5 minutes, turning after the first minute. Remove from heat; transfer to a strainer reserving the cooking liquid.
Place cooked eggplant and zucchini into large bowl. Add chopped roasted peppers, 1/4 cup of the vinegar cooking liquid, freshly chopped Italian parsley and fresh oregano. Pour in garlic oil mixture. Stir gently but thoroughly with a spatula. Cover with plastic wrap and refrigerate for at least 6 hours.
Before serving, drizzle vegetable oil over the mixture.