In a medium pot place cauliflower florets, cover with water and add salt. Bring to a boil on high. Lower to medium and boil additional 10 minutes.
Drain well. Leave a few florets aside. Transfer the remaining florets into a blender or food processor. Add broth and blend.
In a medium pot heat oil and butter on medium. When butter melts lower heat and add flour. Stir continuously until it turns into a roux, about 1-3 minutes. Add blended cauliflower and continue stirring. Add milk and heavy cream and continue stirring. Take the florets you left aside, rip them up into chunks and add in. Bring soup to a boil and remove off heat.
Garnish with parsley.
If the soup thickens too much for your taste use 10 ounces of milk and skip heavy cream.