Heat the butter and oil in a large saucepan, add the onion and fry gently for 5 minutes until just turning golden around the edges. Add the mushrooms and garlic and fry over a high heat for 2–3 minutes until golden.
Stir in the Madeira, stock, rice and thyme, then season with salt and pepper and bring to the boil. Cover and simmer for 30 minutes.
Allow the soup to cool slightly and discard the thyme sprigs. Purée the soup in batches in a blender or food processor until smooth. Return to the saucepan and stir in the milk and cream. Reheat without boiling, then taste and adjust the seasoning if needed.
Make the garnish by heating the remaining butter in a frying pan and slicing any large exotic mushrooms, then add them to the pan and fry for 2 minutes until golden. Ladle the soup into shallow soup bowls and gently spoon the mushrooms into the centre. Garnish with a few thyme leaves and serve with scones (see below).