Rice Cakes:
Preheat oven to 200°F. Line a baking sheet with parchment paper.
Cook rice in water for 40 minutes or until rice is tender and water is absorbed. Cool the rice.
Mix rice, ginger, garlic, scallions, five-spice, egg whites, soy sauce, and flour together in a medium mixing bowl.
Heat a large sauté pan, lightly coated with sesame oil, over medium-high heat. Using a tablespoon, spoon batter into the pan and flatten. Brown the cakes on both sides until golden. Transfer browned cakes to prepared sheet and keep warm in the oven.
Vegetable Topping:
Heat a large sauté pan or wok, generously coated with toasted sesame oil, over very high heat.
Wok char mushrooms, carrots, peas, and broccoli in batches until they are crispy and browned.
Whisk ginger, garlic, soy sauce, and cornstarch together. Return vegetables to hot pan and add soy mixture. Stir fry for 1 to 2 minutes to create a thick sauce.
Top each rice cake with vegetables and garnish with sesame seeds, hot sauce, and scallions.