Warm ham slices in a large, non-stick skillet over medium-high heat for 1 - 2 minutes per side.
Heat the oil in a nonstick pan on medium heat. Crack the eggs into the pan, cook until top is nearly set but still glossy, then carefully fold eggs over add cheese to melt.
Toast bread.
To assemble: Place eggs with melted cheese, ham on toast. Serve immediately with sliced apples.