Arrange the flat mushrooms in a single layer in an ovenproof serving dish. Season with salt and freshly ground black pepper.
To make the filling, preheat the oven to 200C/400F/Gas 6.
Chop the stalks from the large flat mushrooms and chop all the Chinese mushrooms. Add to a bowl with the garlic, melted butter, egg yolk, breadcrumbs and the herbs. Season with salt, freshly ground black pepper and a pinch of nutmeg. Divide the filling between the flat mushrooms.
For the cheese sauce, pour the milk into a saucepan with the carrot, onion, peppercorns, thyme and parsley. Place over a medium heat and bring to the boil. Simmer for 4-5 minutes, then remove from the heat, cover and leave to infuse for 10 minutes.
As the sauce infuses, make a roux. Add the flour and butter to a clean saucepan and place over a medium heat. Stir frequently, for approximately two minutes until the roux is thick and well combined, then set aside to cool.
Strain the milk to remove the vegetables and herbs. In a pan, bring the milk to the boil then whisk in the roux. Whisk constantly until you have a sauce just thick enough to coat the back of a spoon. Stir in the mustard and the grated cheese. Season to taste with salt and freshly ground black pepper.
Put the butter in a pan over a medium heat and melt. When just until melted, remove from the heat and stir in the breadcrumbs. Set aside to cool.
Spread a little of the sauce over each mushroom and top with the breadcrumbs and the grated cheese.
Bake in the oven for 15 minutes, or until lightly browned on top. If you would like them even crisper, place under a hot grill for a minute or two to finish. Serve immediately.