In a large pot or Dutch oven, melt the butter over medium heat. Add the leeks, celery and garlic and cook, stirring occasionally, for 7 to 8 minutes until the leeks are very tender but not browned.
Add the chopped potato, vegetable broth, water, fresh thyme, bay leaf, and salt and bring to a simmer. Simmer for 20 minutes until the potatoes are tender. Remove the thyme and bay leaf.
Transfer to a blender and blend until smooth. Add the cream and blend again. Taste and adjust seasonings as desired.