Heat 1 Tbsp. sesame oil in a sauté pan. Add garlic and stir until fragrant. Add mushrooms and soy sauce and sauté for 5 minutes, until mushrooms turn golden brown. Remove mushrooms from pan and add grated daikon to the same pan. Simmer for about 10 minutes, stirring occasionally so it does not brown. The daikon will produce liquid, some of which will evaporate. Pour everything (including the liquid) into a large mixing bowl to cool. Add rice flour, starch, sugar and salt to the bowl and stir until well-incorporated. Mix in the mushrooms and scallions. Mixture should be thick but not dry. Add water to loosen it up, if needed. Transfer the mixture into a well-oiled loaf pan and spread it out evenly. Place the pan into a steamer with plenty of water and steam over medium-high heat for 50 minutes. Remove from steamer and let it cool for 30 minutes, then loosen the sides with a spatula and turn it out onto a cutting board.
Use a sharp knife dipped in water, cut cake into squares. Add 2 Tbsp. sesame oil to a non-stick or seasoned cast iron pan over medium-low heat. Fry the cakes on both sides until golden and crispy. Serve hot with soy sauce.