Slice brussels sprouts in half and squeeze gently to separate layers a bit.
Heat light olive oil in a medium saucepan until smoking. Tip in the sprouts. Fry until browned all over, turning every now and then. They should be crispy. Season with a generous pinch of salt and spoon out of the saucepan. Discard oil.
Drop the butter and a quick drizzle of extra olive oil into the pan, add the garlic and anchovies, and leave to melt together on a medium heat. When fragrant, add mushrooms and cook gently. If the mushrooms seem like they are drying out, add a splash of water to get things going, and cook mushrooms through – about 4 minutes.
Turn off heat. Tip sprouts back in and squeeze the whole lemon’s juice over the vegetables and mix everything. Turn onto a warm plate, finely grate (preferably with a microplane) mimolette all over the vegetables until it looks like an orange cloud.
Sprinkle piment d’espelette liberally over the cheese.
Pour a chilled glass of chardonnay and serve.
