Mix scallions, ginger, 1⁄4 cup oil and sherry or rice wine vinegar in a bowl. Season with salt (I use about 1⁄2 teaspoon fine sea salt). Set aside.
Heat a large frying pan over medium high. Add 1 to 2 tablespoons oil; you’ll want to coat the bottom with a thin layer of oil all over. Nonstick pan (as I used) are more forgiving here, so you can use the lower amount. Heat the oil until it’s hot, another minute, then scatter half the rice over the surface; it’s okay if small clusters remain. Season lightly with salt and do not touch it. In 3 to 5 minutes, the underside will become golden brown and crisp. Use a spatula to flip it in sections then fry on the other side until it is also crisp. Divide between two bowls and repeat with remaining rice, dividing it between two remaining bowls.
If there isn’t enough oil left in the pan (you want a thin layer), add another splash and heat this on high heat. Add eggs one at a time and season lightly with salt and pepper. Cook until brown, lacy, and crisp underneath, and the whites are opaque, bubbly and dramatic and the edges are brown. You can spoon some oil from the pan over the egg whites to help them cook faster. Place one egg on each bowl of rice.
Arrange some cucumbers and carrots to each bowl. Spoon 2 tablespoons vinaigrette onto each bowls. Drizzle each egg with a half-teaspoon of tamari and toasted sesame oil, letting it roll onto the other ingredients, plus hot sauce to taste. Eat immediately. Repeat frequently.