Wash and chop broccoli florets. Using a peeler, peel about half of the stem of the broccoli and chop the stems. Set aside. Peel and dice potatoes, set aside.
Heat olive oil in medium sauce pot. Add leeks and cook for about 5 minutes, until the leeks become transparent. Add garlic and sauté for 2 minutes until softened.
Add broccoli stems and larger florets, potatoes, and vegetable broth. Bring to a boil and then reduce heat to simmer. Cover partially with a lid and cook for about 10-12 minutes until the broccoli stems and potatoes are almost cooked. The last 5-7 minutes add the florets and cook until tender.
Remove from heat and using a hand-blender and blend until vegetables are pureed and the texture is creamy. Option is to use a food processor or blender.
Season with salt and pepper. Garnish with scallions greens, chopped broccoli florets and drizzle with olive oil.