To make the mushrooms, preheat the oven to 180C/160C Fan/Gas 4.
Put the miso paste, minced garlic, soy, sake, ginger and butter in a saucepan and bring to the boil. Put the mushrooms in a roasting tin and pour the miso mixture over the mushrooms. Cover with kitchen foil and bake for 30 minutes.
Remove the mushrooms from the oven. Reserve the liquid from the tray (it should be quite thick, if not, transfer to a small saucepan and simmer to reduce to a glaze). Set aside and keep warm. Reserve some of the ginger strips too.
Toast the slices of sourdough, then rub with the cut side of the halved garlic clove and drizzle with the olive oil.
Slice the mushrooms, spoon them onto the toast and drizzle over the glaze. Scatter over the sesame seeds, chives, spring onions and ginger strips and serve immediately.