Preheat the oven to 200°C/400°F/gas 6. Halve the tomatoes and place cut-side up in a large roasting tray. Break the garlic bulb into cloves. Peel and slice the onions into 3cm wedges, then scatter both into the tray.
Sprinkle with oregano, season with sea salt and black pepper, then drizzle with oil. Roast for 50 minutes to 1 hour, or until the tomatoes are soft and sticky. Scrape everything from the tray into a large pan, picking out and squeezing in the garlic, discarding the skins. Pour in the stock, then roughly chop and add the basil stalks with most of the leaves.
Cut the ciabatta loaf in half and tear one half into the soup. Bring to the boil, then simmer for 10 minutes. Meanwhile, put a griddle pan on a high heat. Slice the remaining ciabatta and griddle until lightly charred on both sides. Add 1 splash of red wine vinegar to the soup, then blitz using the bamix® multi-purpose blade until fairly smooth.
Ladle into bowls, drizzle with extra virgin olive oil and scatter with the remaining basil leaves, serving the griddled ciabatta on the side.