Combine eggs, flour, 1 tablespoon sugar, baking powder, and salt in a large bowl; gradually mix in milk, stirring constantly. Add vanilla, melted butter, and 1/2 teaspoon nutmeg. Let batter stand for 30 minutes or overnight.
Preheat the oven to 425 degrees F (220 degrees C).
Melt butter in a 10-inch oven-proof skillet, brushing butter up on the sides of the pan. Combine 1/4 cup sugar, cinnamon, and 1/2 teaspoon nutmeg in a small bowl; sprinkle sugar mixture over the butter. Line the pan with apple slices. Sprinkle the remaining 1/4 cup sugar over apples. Place pan over medium-high heat until the mixture bubbles, then gently pour batter mixture over apples.
Bake in the preheated oven for 15 minutes. Reduce heat to 375 degrees F (190 degrees C) and bake for 10 minutes more. Slide pancake onto a serving platter and cut into wedges.