Place the rice in a strainer and rinse under cold running water until the water is fairly clear, about 5 minutes. Shake the water out and allow the rice to dry in the strainer for 15 minutes.
Put the rice in a pot with exactly 3 cups of water and cook covered over high heat until it starts to foam, about 5 minutes. Reduce the heat to low and cook until tender, about 15 minutes. Turn off the heat and sprinkle with 1/4 cup mirin. Replace the lid and allow the rice to steam for 15 minutes. Place in a bowl and cool to room temperature.
To prepare the sushi, place a bamboo sushi roller flat on a table with the bamboo reeds horizontal to you. Sprinkle lightly with water. Place 1 nori sheet on top, smooth side down, and moisten lightly with mirin. With damp hands, press 1 1/4 cups rice flat on top of the nori, leaving 1 1/2-inch edges on the top and bottom, but pressing all the way to the sides. Make sure the rice is pressed even and smooth.
Spread 1/4 teaspoon of wasabi paste in a horizontal stripe near the lower edge of the rice. Over the wasabi, lightly sprinkle the red onions in a horizontal stripe. Place strips of carrots in a horizontal stripe, on top of the wasabi and onions, and follow by piling the red and yellow peppers, scallions, and cucumbers on top, making a tight, straight bundle of vegetables. Place 1 layer of pickled ginger slices on top.
To roll the sushi, pick up the near edge of the bamboo roller and hold it with the nori, then pull them up and over the vegetable bundle until the nori reaches the rice on the other side. Press the roller to make a round bundle, then roll the bundle to the far edge of the nori and press again to make a round bundle. (The nori should totally enclose the rice and vegetables in a round tube, but the ends will have rice and vegetables sticking out.) Repeat the process with the remaining ingredients. Keep the rolls under a damp towel and refrigerate until ready to serve. To serve, slice off the ends with a very sharp knife and slice each roll into 8 equal pieces.
Meanwhile, for the sushi dipping sauce, combine the wasabi powder and water to make a paste. Mix in the red pepper flakes, ginger, scallions, vinegar, soy sauce, and sesame oil. Serve the sushi at room temperature with the dipping sauce.
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