In medium bowl, beat eggs with whisk; season with salt and pepper. If needed, melt butter in skillet over medium heat. Pour eggs into skillet. Allow to set 1 minute, then slowly stir in buttermilk and 1/4 cup of the cheese. Use spatula to fold eggs over while gently shaking skillet with other hand. As soon as there is no more liquid remaining around bottom of skillet, remove from heat.