Wipe the mushrooms caps clean with a damp paper towel. Slice mushrooms and set them aside.
Heat oil and butter in a large, heavy pot over low heat. Add onion and cook until wilted, stirring occasionally (10-12 minutes). Add garlic and cook 2 more minutes.
Add mushrooms and cook, uncovered, stirring frequently for 15 minutes. Season with thyme, nutmeg, salt, and pepper.
Add chicken broth and bring to a boil. Reduce heat to medium, cover, and simmer for 30 minutes. Remove pot from heat and let cool to room temperature.
Puree the soup, in batches, in a food processor or blender until smooth, then add the cream gradually. Mix well. Return the soup to the pot and adjust the seasonings to taste.
Before serving, heat the soup over very low heat (do not boil). Garnish with chives and serve piping hot.