Heat butter or olive oil in a large, heavy 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 a 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 a large saucepan. Season to taste with salt.
Bring to a simmer before serving.
If the soup is too thick, add some more broth.
Ladle soup into bowls. Garnish with chives and serve.