To make the sauce. In a small bowl, combine the soy sauce, toasted sesame oil, hoisin sauce, and chili flakes.
Heat 1 tablespoon oil in a large skillet over medium heat. Add the eggs (if using), season with salt and pepper, and let cook until the edges start to set, 1-2 minutes. Roughly scramble the eggs. Remove from the heat and transfer to a plate.
Return the skillet to medium-high heat. Add 2 tablespoons oil. When the oil shimmers add the mushrooms and cook, stirring occasionally, until the mushrooms are crisping on the edges, about 5 minutes. Season with salt and large pinch of pepper. Stir in the green onions, ginger, garlic, and bok choy. Cook another 2-3 minutes, until the mushrooms are caramelized. Remove from the heat and transfer the mushrooms and greens to the plate with the eggs.
Return the skillet to medium-high heat and add the remaining 2 tablespoons oil. Add the chicken and cook until browned, 5 minutes. Stir in 2 tablespoons of the sauce, cook another 1-2 minutes. Add the rice and cook, stirring occasionally, until toasted, 4 to 5 minutes. Stir in the remaining sauce, toss, cook another 1 to 2 minutes. Stir in the mushroom, bok choy, and eggs. Remove from the heat. Add the basil or cilantro.
Divide the rice amoung bowls and top with additional green onions.
