Melt butter in skillet over medium heat. Add leeks and cook for 3 minutes until soft. Add garlic and cook 1 minute more. Scrape leeks and garlic into slow cooker.
Cut off the broccoli florets and chop them. Cut two inches off bottom of the stem. Peel the remainder of the stems and then slice and chop them. Add chopped broccoli to the slow cooker, along with the olive oil, vegetable broth, thyme, white wine and 2 tablespoons of lemon juice. Add salt and pepper to taste. Cover and cook on LOW for 5-6 hours.
Meanwhile, in a small bowl, mix the sour cream, remaining 2 tablespoons lemon juice, lemon zest, chives and Parmesan cheese. Season it with salt and pepper. Refrigerate until ready to use.
When the soup is finished, transfer it in batches to a food processor or blender and puree until smooth. Taste the soup and adjust seasonings if necessary. Stir in half of the lemon chive cream. Ladle into bowls and serve with a dollop of remaining cream and some shredded cheddar cheese, if desired.