Whisk the first three ingredients in a bowl. Mix in the cheese, ham and half the chives. Melt the butter in a large non-stick skillet over medium heat. Add the eggs. As mixture begins to set, gently move a spatula across the bottom and sides of the skillet to form large, soft curds. Cook until the eggs are cooked, but still moist, with no visible liquid egg remaining. Sprinkle portions with remaining chopped chives.