Preheat oven to 350°. In a 6-qt. Dutch oven, combine apples, 3/4 cup sugar and 1/2 teaspoon cinnamon. In a bowl, whisk flour, brown sugar, remaining 1/4 cup sugar, baking powder, salt and remaining 1/4 teaspoon cinnamon; stir in eggs (mixture will be lumpy). Spoon over apples. Drizzle butter over batter (do not stir). Cover and bake until lightly browned and apples are tender, 45-50 minutes. Serve warm with ice cream, if desired.
