Heat butter and oil in a heavy-bottomed pot over low heat. Add onion and garlic, cover, and cook until soft, about 20 minutes.
Increase heat to medium and stir in chanterelle mushrooms. Sprinkle with flour and pour in boiling water, stirring constantly. Season with chicken bouillon, bay leaves, thyme, white pepper, and nutmeg and bring to a simmer. Cover and simmer until mushrooms are soft and flavors are well combined, 15 to 20 minutes.
Remove bay leaves. Puree chanterelle soup with an immersion blender until smooth.