To make this soup even more refined, pass the tomatoes through a food mill to remove the seeds before adding them to the pan. Canned whole plum tomatoes are the best choice for this recipe, since they are packed at the height of ripeness and prepeeled.
In a large pot over medium-high heat, combine stock, tomatoes, matzo, garlic, basil, and olive oil; bring to a boil. Lower heat and simmer 30 minutes, stirring often to crush the matzo into the stock. Discard basil leaves and season with salt and pepper. Ladle into bowls and garnish with chopped basil and a drizzle of olive oil. Serve hot.