Sauté green garlic in butter. Add leeks and continue cooking, until translucent, being careful not to brown ingredients. Season with salt and pepper.

Peel white asparagus and cut into one-inch lengths, reserving the tips for garnish. Add white wine to the leeks and garlic and reduce until almost dry. Add white asparagus and vegetable stock. Simmer until all ingredients are tender. Add heavy cream and simmer for 10 more minutes. Purée in batches if necessary and strain. Return to saucepan and add asparagus tips.

Check seasoning, add salt if necessary, and finish with the fresh thyme. When asparagus tips are tender, pour soup into bowl and garnish with chopped chives.