Roughly chop the white part of the leek and place into a large saucepan, along with the butter and garlic.
Saute the leeks over low heat until they are beginning to turn translucent. Add the cream.
Cut the broccoli into evenly sized florets and place into the saucepan.
Add the chicken stock and stir. Ensure that the broccoli is mostly covered.
Simmer on low to medium heat for 8 minutes. If you cook the broccoli too quick, it will discolor and turn the soup an off brown color. The broccoli is cooked when it is easy to break up with a spoon.
Using a stick blender, carefully blend the soup until no lumps are remaining.
Stir through the salt, pepper, and parsley. Adjust seasoning to taste. Enjoy.