Chop green garlic. In a soup pot, melt butter over medium-high heat. Add green garlic and sauté until translucent, about 3 minutes. Add scapes, thyme, salt and pepper, and sauté for 5 minutes.
Stir in potato and broth, reduce heat to medium, and simmer until scapes and potatoes are tender, about 20 minutes. Add half-and-half, and purée soup with an immersion blender or pour into a regular blender. Stir in the lemon juice and season with more salt and pepper. Garnish with nutmeg and thyme leaves, and serve hot.