Place the eggs in a medium-sized bowl and beat until the yolks and whites are thoroughly combined. Mix in the milk, ham, cheese, salt and pepper. Melt the butter in a large non-stick skillet set over medium heat, and then add the egg mixture. As the egg mixture begins to set on the bottom, gently move a heatproof spatula across the bottom and sides of the skillet to form large, soft curds. Continue cooking until the eggs are cooked, but still moist, with no visible liquid egg remaining. Sprinkle with chives and serve.