Let's cook.
In a small bowl, whisk together the eggs, milk, salt, and pepper until just combined and slightly frothy.
Melt 1/4 tablespoon of butter in an 8-inch non-stick skillet over medium heat. Add the thinly sliced apple and sauté for 3-4 minutes, until softened and lightly caramelized. Remove apples from the skillet and set aside.
Add the remaining 1/4 tablespoon of butter to the same skillet and swirl to coat the bottom. Pour the egg mixture into the hot skillet.
As the edges of the omelette begin to set, gently push the cooked egg from the edges towards the center with a spatula, tilting the pan to allow uncooked egg to flow underneath.
When the top is mostly set but still slightly moist, arrange the sautéed apples and brie cheese over one half of the omelette.
Cook for another 1-2 minutes, allowing the brie to soften. Carefully fold the other half of the omelette over the filling.
Slide the omelette onto a plate and serve immediately.
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