Bring apple cider, butter, brown sugar, vanilla, and cinnamon to a boil over medium-high heat in a large saucepan. Reduce heat and boil gently, stirring occasionally, until thick and syrupy, 30–45 minutes.
Dutch Baby:
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 and pour batter over.
Bake until pancake is puffed up and golden brown around the edges and center is slightly set, 12–15 minutes.
Serve drizzled with apple cider syrup.
Recipe by Bent Arrow Acres at https://www.bentarrowacres.com/apple-dutch-baby/