Add the chicken stock in a medium saucepan and bring to simmer. Remove from heat and add the saffron threads. Set aside to steep.
Heat the olive oil in a medium pot over medium-low heat. Add chopped onions & celery; sauté until quite tender but not brown (about 5 minutes). Add the garlic and cook another minute.
Add the cauliflower & potato; stir to coat.
Add saffron stock. Bring to a boil over high heat.
Reduce heat, cover, and simmer until the cauliflower & potato are tender (about 20 minutes).
Using a hand blender or food processor, puree the soup until smooth.
Season to taste with salt and pepper. Garnish with chopped parsley and serve.
Notes
To make this soup suitable for vegetarians, simply swap the chicken stock for vegetable stock.