Melt the butter in a saucepan and cook the onions for about 4 minutes, until softened. Add the ginger and continue to cook an additional 2 minutes. Add the avocado, lime juice, and chicken stock and whisk to combine. Simmer soup over medium-low heat for about 5 minutes. Add the green onion and transfer the soup to a blender and puree, in batches if necessary, until very smooth. Stir in the half-and-half and salt and pepper, to taste. Chill thoroughly before serving.

To make the lime crema, stir together the sour cream, lime juice, garlic, and salt. When the soup has chilled, garnish each portion with a generous dollop of crema.