Whisk the eggs and milk with the salt and pepper in a bowl. Place a saucepan in a large skillet, and add enough water to the skillet to come up about one inch on the saucepan. Add the butter to the saucepan over medium-low heat. Stir in the egg mixture and cook, stirring often, until the eggs are just softly cooked. Add the cream cheese and continue to cook, stirring often, until eggs are cooked and the cream cheese melts, about 2 minutes.