Beat the eggs in a medium bowl. Heat 1 teaspoon oil in a non-stick skillet over medium heat. Add the eggs and stir with a wooden spoon or spatula until fully cooked, about 2–3 minutes. Remove from the skillet and set aside.
Heat the remaining 1½ tablespoons oil in a large, deep non-stick skillet or wok over medium-high heat. When the oil is hot, add the chicken. Arrange it in a single layer and sprinkle with a pinch of salt. Cook for 1–1½ minutes. Flip the chicken in sections and arrange it in one layer again. Cook another 1–1½ minutes, then stir well.
Add the shrimp and diced white onions to the pan. Cook for 2 minutes, stirring almost constantly.
Add the cubed ham, garlic, and ginger powder. Stir well and cook for 1–2 minutes, stirring frequently, until the shrimp is fully cooked (it will be pink, curled, and no longer translucent).
Add the white rice to the skillet and stir well to combine. Cook, stirring constantly, for 1–2 minutes, until the rice is hot and steaming.
Stir in the scrambled eggs and bean sprouts, mixing well.
Pour in the soy sauce, stirring constantly to coat all the ingredients evenly. Lower the heat to medium-low and continue stirring until the rice is evenly coated.
Sprinkle in the green onions and stir. Reduce the heat to low, cover the skillet, and cook for 5–10 minutes to let the flavors meld.
Taste the rice and add salt if needed. (We did not add extra salt.)
Serve and garnish with extra green onions, if desired.