Bring water to boil. Add oatmeal, reduce heat a little and let it cook for about 3 minutes, until all liquid is absorbed. Turn off heat and stir in cheese, a small pinch of salt, and pepper.
Heat a nonstick pan with ½ teaspoon of coconut oil over medium-high heat. Add vegetables and cook for 2 to 3 minutes, until they soften. Spoon vegetables over cooked oats. Reduce heat to medium.
Add remaining ½ teaspoon of oil and fry egg. Cook until the whites are no longer translucent and serve over oatmeal.
Top with chopped walnuts, green onions, and za'atar, if you like.
