Place the apple slices in a small, nonstick skillet over medium-high heat. Cook until they soften and start to brown, about 5 minutes. Add the maple syrup and cinnamon, toss to coat, cook for another 30 seconds then remove from the heat. Set aside.
Separate the eggs placing the whites in one mixing bowl and the yolks in another. To the yolks add the almond milk and a pinch of salt and pepper, whisk to combine.
With a handheld mixer or whisk, beat the whites just until soft peaks form.
Fold the egg whites into the yolk mixture. Melt the coconut oil in a 5 inch, non-stick pan over low heat. Add the egg mixture to the pan and cook for 3 minutes. Sprinkle the cheese over the top, layer on the cooked apples and cover the pan. Cook for another 5 - 6 minutes or until the eggs are set and the bottom is golden brown. Slide the omelette onto a plate and fold the one half of the omelette over the other. Serve immediately with the chopped walnuts on top if desired.