Preheat the oven to 400°. Thinly slice the scallops crosswise. Spread them in 4 ovenproof soup plates. Melt the butter in a medium saucepan. Brush the scallops with some of the butter and season with salt and pepper.
Add the mushrooms to the remaining butter in the saucepan. Season with salt and pepper and cook over moderately high heat until lightly browned, about 5 minutes. Add the leek and ginger and cook, stirring, until wilted, about 3 minutes. Add the stock and bring to a boil. Season with salt. Keep hot.
Bake the scallops in the oven for about 30 seconds, or until the bowls are hot. Pour the hot soup over the scallops, garnish with the cilantro and serve.