In a large mixing bowl, whisk together the eggs, flour, sugar, baking powder, and salt until well combined. Gradually stir in the milk, melted butter, vanilla extract, and ground nutmeg, ensuring a smooth batter without lumps. Allow the batter to rest for at least 30 minutes, or refrigerate overnight.

Preheat your oven to 425°F (220°C). In an oven-proof skillet, melt 2 tablespoons of unsalted butter over medium heat, swirling to coat the pan sides. In a small bowl, mix sugar with cinnamon and nutmeg, then sprinkle this mixture over the melted butter. Arrange your sliced tart apples in a single layer, allowing them to cook for about 5 minutes until tender and fragrant.

After the apples have softened, carefully pour the rested batter over the arranged apples, avoiding stirring. Place the skillet in the preheated oven and bake for 15 minutes until the edges are puffing up and golden. Reduce the temperature to 375°F (190°C) and bake for an additional 10 minutes until fully puffed and golden brown.

Once baked, remove the skillet from the oven and gently slide the pancake onto a large platter. Cut into wedges, serving warm. Dust with powdered sugar or a sprinkle of cinnamon for extra sweetness.