1. Preheat oven to 375F. Mark 5.
2. Brush the mushroom caps with melted butter. Place them, hollow-side up, in the roasting tin. Sprinkle lightly with salt and pepper.
3. Sauté the onions in butter and oil for 3 to 4 minutes without browning. Then add the shallots or spring onions and mushroom stems.
4. Add the optional Madeira and boil it down rapidly until it has almost entirely evaporated.
5. Away from heat, mix in the breadcrumbs, cheeses, parsley, tarragon, and seasonings. A spoonful at a time, blend in just enough cream to moisten the mixture but keep it sufficiently stiff to hold its shape in a spoon. Correct seasoning.
6. Fill the mushroom caps with stuffing. Top each with a pinch of cheese and drops of melted butter.
7. Bake in upper part of a preheated, 375F., Mark 5 oven for 15 to 20 minutes, or until caps are tender and stuffing has browned lightly on top.