4 ounces lean Black Forest ham, cut into 1/2-inch cubes
3 ounces shredded Gruyere or Cheddar (about 3/4 cup)
1/3 cup chopped fresh chives (about 1/3 small bunch); plus more for garnish
2 teaspoons extra-virgin olive oil
4 large eggs
In a large saucepan, bring 4 1/4 cups water, 1 teaspoon salt, and 1/2 teaspoon pepper to a boil. Stir in the oats, decrease heat to medium, and cook, stirring constantly, for about 7 minutes, or until the oats are mushy and the oatmeal has thickened somewhat. Remove the pot from the heat and stir in the ham, cheese, and chives.
In a large nonstick skillet, heat the oil over medium-high heat. Crack the eggs carefully into the pan and cook for 2 to 3 minutes, or until the whites are set and slightly crispy but the yolk is still runny. 1/4 teaspoon salt, to taste.
Place the oatmeal in separate dishes. Serve with an egg on top and more fresh chives on the side.