In a large nonstick skillet, heat 1 tablespoon oil over medium-high. Add ham, scallion whites, garlic, and ginger; season with salt and pepper. Cook, stirring frequently, until beginning to brown, 2 to 4 minutes.
Add rice, scallion greens, vinegar, and soy sauce. Cook, stirring, until heated through, 2 to 4 minutes. Divide fried rice among four serving bowls.
Wipe out skillet with a paper towel. Heat 1 tablespoon oil over medium. Gently crack eggs into skillet; season with salt, and cook until whites are set, 2 to 4 minutes. Top each bowl of rice with a fried egg.
Instead of peeling ginger root with a knife, scrape off the peel using the edge of a spoon. This way, more ginger goes into your fried rice and less into the garbage.