Halve leeks lengthwise and thinly slice crosswise.
In a large bowl of cold water wash leeks well and lift from water into a large sieve to drain. In a 6-quart heavy kettle cook leeks in butter over moderately low heat, stirring occasionally, until some begin to turn golden, about 40 minutes. Add remaining 3 cups broth and bring soup just to a boil. Season soup with salt and pepper. Serve soup, garnished with chives, with cheese croutons.