Coat a large saute pan generously with canola oil (it is FRIED rice) and toss in the onion and carrot; bring the pan to medium-high heat. Cook for 6 to 7 minutes, stirring frequently.
Stir in the ginger, garlic and scallion whites and cook for 1 minute more.
Toss in the chicken and cook until no longer pink and beginning to brown, about 4 minutes. Add the edamame and chopped cilantro and increase the heat to high. Add the rice to the pan and stir to combine, then let sit and get a little crunchy on the bottom. Toss occasionally, but be sure to give it a chance to get a little crispy, 3 to 4 minutes, and then repeat—resist the urge to stir it too much or it will just get soggy.
In a small bowl, combine the soy sauce, vinegar, and sambal, if using, and add it to the rice, cooking over high heat, 1 to 2 minutes.
Meanwhile, coat a medium nonstick saute pan lightly with canola oil, add the eggs, and bring to medium heat. Cook the eggs until the whites are cooked through but the yolks are soft and runny, 3 to 4 minutes.
Transfer the rice to serving plates and top each with an egg, a sprinkle of the whole cilantro leaves, and scallion greens.