Make the sauce by mixing together the yogurt, mayo and 1/4 teaspoon dill. Set aside.
Snap off the tops of the haricot verts. If using regular green beans, you may need to pull of the stringy fiber on both sides of each pod too.
Cut off the root ends of the bunashimeji. If using other mushroom variety, trim as needed and, if they are large, cut into small pieces.
Heat the butter in a frying pan. Add the haricot verts, mushrooms and garlic. Toss around for a few seconds. Sprinkle with salt and pepper. Pour in a tablespoonful of water. Cover the pan, turn down the heat to low and allow the mushrooms and beans to cook for three to four minutes or until done.
Transfer the cooked mushrooms and haricot verts to a shallow bowl. Drizzle the sauce over them. Sprinkle in the rest of the dill and as much cayenne as you like.
Serve the steam-fried mushrooms and green beans at once.