Break the cold rice into loose, separate grains with your hands or a fork. If using fresh rice, cool it completely before frying.
Heat a wok or 12-inch skillet over high heat and add 3 tablespoons oil. Heat until shimmering, 1–2 minutes.
Crack the eggs into the pan. Don't stir for 2–3 seconds; let the bottoms set slightly. Break them up with a spatula into distinct pieces, not a paste, and cook until fully set.
Add the diced ham and stir-fry 10–15 seconds until coated in oil and fragrant.
Add the rice and toss over high heat so it heats evenly and picks up a toasted flavor. Lower the heat slightly once the rice is in, and press and toss until every grain is coated and hot, about 2–3 minutes.
Add salt, chicken bouillon powder, and five-spice powder. Toss until evenly distributed. Taste and adjust salt.
Add the scallions, toss once or twice, and turn off the heat. Serve immediately.