Preheat the oven to 425 F. (218 C.) and line a rimmed baking sheet with parchment paper.
Halve the tomatoes and put them on the baking sheet, cut side up. Add the onions and garlic, sprinkle with salt and pepper and toss well with olive oil to coat evenly.
Roast for 20-30 minutes or for as long as it takes to caramelize the onions and for the tomatoes to roast, becoming soft and somewhat jammy.
Add everything into a medium-sized pot and add the wine. Simmer at a low boil for 10 minutes, allowing the mixture to reduce a bit. Using a food mill, fitted with a fine setting, mill the contents to remove the tomato skins and seeds and return to the pot.
Pour in the chicken broth and the roughly chopped basil and oregano. Bring to a low boil.
Cut the loaf of ciabatta bread in half and remove crust. Roughly tear into pieces. Add the torn bread to the simmering pot. Simmer for 10 minutes more.
Using a wire whisk, stir the contents of the pot. The bread should have lost its shape by now and will begin to thicken the soup. It’s ok to leave the pieces somewhat intact, if a more rustic soup is preferred. For a smother soup, use a hand-held blender to blast the pieces. Soup should be thick almost bisque-like, but still fluid and silky. Thin with more broth or a small amount of water if necessary. Taste and adjust seasonings.
Tear or slice remaining ciabatta bread and toast until lightly charred. Use a brustolina or broiler (optional).
Ladle soup into bowls. Add a few pieces of the extra toasted bread to each bowl. Drizzle with extra virgin olive oil and serve. Garnish with basil.