Preheat the oven to 500F. In a large bowl, combine the tomatoes, vinegar, garlic, 1/4 cup of the olive oil, and a generous sprinkle of salt and peppers. Transfer the mixture, along with any accumulated juices, to a large rimmed baking sheet. Arrange the tomatoes in a single layer, skin side down, and roast until charred on the edges, about 40 minutes. Set aside and cool slightly, then slip the skins off the tomatoes.
In a large saucepan or small stockpot over medium heat, heat the remaining 2 tablespoons of olive oil. Add the onions and cook, stirring often, until very soft, about 10 minutes. Add the basil, parsley, and sage and cook, stirring occasionally, for about 1 minute. Stir in the roasted tomatoes, along with any accumulated juices, and 5 cups of water. Bring to a boil, lower the heat to a simmer, and cook gently to allow the flavors to blend, about 8 minutes. Add more salt and pepper to taste. Serve hot.