Preheat oven to 200°C and line a baking tray with parchment.
Boil 100g butter, salt, and 300ml water in a saucepan.
Stir in flour and thyme until a smooth dough ball forms.
Beat in eggs gradually until the dough is stiff and glossy.
Place four 10cm dough blobs on the tray and sprinkle with parmesan.
Bake for 30 minutes at 200°C, then move to bottom shelf for 10 minutes.
Split one side of each bun to let steam escape and cool on a rack.
Sauté shallots in butter and oil until soft.
Cook mushrooms, garlic, and thyme for 10 minutes until liquid evaporates.
Simmer with sherry and crème fraîche for 10 minutes until reduced.
Stir in lemon juice, parsley, and seasoning.
Halve the buns, fill with the mushroom mixture, and serve warm.