Put the rice in a small saucepan with 1 1/2 cups water. Set the pan over high heat and bring the water to a boil.

Cover the saucepan, turn the heat to low, and cook the rice for 15 minutes. When the time is up, turn off the heat and let the pan stand, still covered, for 5 minutes.

Put the grated zucchini in a colander set in the sink. Sprinkle it lightly with salt and leave it for 5 minutes so some of the water drains away.

Put the sliced cucumber in a medium bowl. Add 2 tablespoons of the rice vinegar, a pinch of salt, and a small pinch of sugar, then toss and set the bowl aside.

Pour the remaining 1 tablespoon rice vinegar and 3 tablespoons of the soy sauce into a small bowl. Add 1 tablespoon water, stir, and set this dipping sauce aside.

Gather the zucchini in your hands or in a clean kitchen towel and squeeze out as much liquid as you can. Transfer the squeezed zucchini to a large bowl.

Add the grated carrots, the scallion whites, and about half of the scallion greens to the large bowl with the zucchini.

Add the beaten eggs, the flour, the remaining 1 tablespoon soy sauce, and 3/4 cup cold water to the large bowl. Stir until you have a thick batter and the vegetables look evenly coated.

Uncover the rice and fluff it with a fork right in the saucepan. Add the thawed edamame and the remaining scallion greens, stir, and cover the pan again to keep it warm.

Set a large nonstick skillet over medium-high heat. Add 3 tablespoons of the oil and heat it until the oil looks shiny and moves easily across the pan.

Scoop half of the batter into the skillet in 4 mounds. Press each mound gently with the back of a spoon so it spreads into a pancake about 4 inches wide.

Cook the fritters for 3 to 4 minutes on the first side. They are ready to turn when the edges look set and the bottoms are deep golden brown.