Thinly slice the leeks. Heat the oil in a large heavy-bottomed pot. Cook the leeks slowly in the olive oil until the leeks are tender but not browned.
Meanwhile, either chop the tomatoes or puree them in a medium bowl with a hand-held immersion blender, depending on the desired consistency. Mince the garlic.
When the leeks are tender, add the tomatoes and garlic and stir over moderate heat for 3 minutes.
Add the vegetable broth. Bring to a boil, then add the rice, herbs and saffron. Season to taste with salt and pepper.
Simmer, partially covered, for 30 minutes.
Carefully taste for seasoning, adding pinches of sugar to bring out flavor and counteract acidity, and small amounts of tomato paste if needed for color and taste.
Serve garnished with fresh basil.
