How to Make It
Heat butter in a large nonstick skillet over medium heat. Add ham and sauté until browned.
Meanwhile, in a large bowl, whisk together the eggs, milk, 1 teaspoon kosher salt, and 1/4 teaspoon pepper. Pour into the pan and cook, stirring occasionally, to desired doneness, 4 to 5 minutes, adding cheddar and chives just before the eggs are set.