Heat butter or olive oil in heavy large stockpot over medium heat.
Add chopped onions and sauté until very tender but not brown, about 10 minutes.
Add cauliflower pieces; stir to coat and sauté for 2 minutes.
Add saffron and stir, then add broth.
Bring to simmer over high heat.
Reduce heat, cover, and simmer until cauliflower pieces are very tender, about 30-40 minutes.
Working in batches, purée cauliflower mixture in a blender until smooth.
Transfer cauliflower purée to large saucepan. Season to taste with salt.
Bring to simmer before serving.
If the soup is too thick, add some more broth.
Ladle soup into bowls.
Garnish with chives and serve.