Preheat the oven to 350°F. Generously spray a standard 12-cup muffin pan (a nonstick pan is highly recommended) with nonstick cooking spray.
In a large bowl, whisk together the eggs, milk, and salt and pepper to taste (I add ½ teaspoon kosher salt and ¼ teaspoon pepper). Note: Using a bowl with a pouring spout or even an extra-large liquid measuring cup will make it easier and less messy to pour in the next step.
Pour the egg mixture into the muffin cups, making sure each cup has about the same amount (the cups should be two thirds to three quarters full at this point).
Evenly divide the diced ham among the muffin cups.
Evenly divide the cheese among the muffin cups.
Bake for 20 to 25 minutes or just until the eggs are set (the center should no longer jiggle, and a knife inserted in the center will come out clean). The muffins will be very puffy and tall at this point.
Allow the muffins to cool for a few minutes before serving. Note: They will deflate as they cool; this is normal. If you used a nonstick pan sprayed with nonstick cooking spray, they should come out of the pan very easily. If needed, carefully run a knife along the edges of the muffins to loosen them up.
Sprinkle with chopped fresh chives, if desired, and enjoy!