Beat the eggs with the milk and 1/4 teaspoon salt in a small bowl. Stir the ham and cheese together in another small bowl.
Heat a Japanese rectangular omelet pan over medium heat until hot. Brush with little bit of oil. Add just enough of the egg mixture to coat the bottom of the pan when tilted. Let the egg cook until just set on the bottom, then use chopsticks or a rubber spatula to roll the sheet of egg into a log shape and push it to the far end of the pan. Brush the pan with more oil and again add just enough egg to coat the bottom when tilted, this time lifting up the rolled egg so that the raw egg flows underneath it. (If the egg is browning or setting too quickly, control the heat by lifting the pan off the burner for a moment.) When the underside is just set, roll the log towards the handle of the pan, then push the log back to the far end. Repeat; when you have made 3 layers, make another layer in the same manner and add half the ham and cheese. Make another layer, using the rest of the ham and cheese. Finish making the omelet in the same manner with the remaining egg.
Turn the omelet out onto a plate, sprinkle with chives and serve.
If the egg is browning or setting too quickly, control the heat by lifting the pan off the burner.