Heat the oil in a large saucepan over medium-high heat. Add the leek and cook, stirring often, until starting to turn golden, about 4 min.
Add the cauliflower, apples, broth and 2 cups (500 mL) water. Bring to a boil. Reduce heat and simmer until apple and cauliflower are fork-tender, about 15 min.
Using a hand-held blender, or food processor, process the cauliflower mixture until creamy and smooth, about 2 min. Return soup to saucepan and warm over medium-low heat until heated through. Divide soup among 6 bowls and garnish with parsley.