In a large heavy-bottomed soup pot, melt butter over medium-high heat. When butter is hot and bubbly, add leeks, garlic and carrots and cook until softened, about 3 minutes. Add potatoes, stir well and cook 2 minutes.
Add stock, bay leaf, celery seed, thyme and basil. Bring to a boil. Reduce heat to medium and cook until potatoes are barely tender, about 15 minutes. Add broccoli and cook about another 10 minutes, until tender.
In a blender or food processor, puree soup in batched until vegetables are well belnded. Pour soup back into pot and stir in cream. Season to taste with black pepper and dash cayenne pepper. Cook over low heat until heated through. Do not boil. Stir in cheese just before serving. Taste, and adjust seasonings.