DO AHEAD: Syrup can be made 1 week ahead. Let cool; cover and chill. Bring to room temperature before using. Preheat oven to 425°. Whisk eggs, milk, flour, vanilla, salt, and ½ tsp. cinnamon in a medium bowl until smooth. Melt 2 Tbsp. butter in a 10” skillet, preferably cast iron, over medium heat. Add apple and sprinkle with brown sugar and remaining ½ tsp. cinnamon. Cook, tossing often, until apple is coated and softened, about 4 minutes. Transfer to a plate. Wipe out skillet and heat in oven until very hot, 8–10 minutes. Carefully add remaining 2 Tbsp. butter to skillet, tilting to coat bottom and sides. Add apple to center of skillet; pour batter over. Bake until pancake is puffed and golden brown around the edges and center is set but still custardy, 12–15 minutes. Serve drizzled with apple cider syrup.