Blanch spinach leaves in a large saucepan of boiling water, then refresh in iced water. Squeeze well to remove excess water then chop finely. Set aside. Pound sesame seeds with sugar until pasty. Mix in soy sauce and sesame oil, then toss with spinach. Set aside.
Preheat a lightly greased barbecue grill on medium-high heat. Toss mushrooms in oil and sprinkle with salt. Arrange mushrooms on barbecue grill and cook for 3 minutes on each side, until just tender. Transfer to a board and cut into thick slices. Arrange spinach on serving plates, top with sliced mushrooms and sprinkle with shichimi powder and serve.