1. Bring apples and cider to a boil in a large pot. Reduce to a simmer; cook, stirring occasionally, until apples begin to soften and liquid has reduced, 40 to 50 minutes. Add 1 cup water; cook, mashing apples slightly, until liquid has reduced, about 10 minutes. Add 2/3 cup granulated sugar and 1/2 cup water; simmer until apples are very soft and coated in syrup, about 15 minutes. Let cool completely.

2. Preheat oven to 375 degrees. Butter two 9-inch round cake pans. Line bottoms with parchment paper, and butter parchment. Dust with flour; tap out excess. Set aside.

3. Put butter and the remaining cup sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until creamy, about 3 minutes. Reduce speed to low; mix in egg, molasses, buttermilk, baking soda, flour, spices, and salt.

4. Divide batter evenly between prepared pans. Bake until a cake tester inserted into centers comes out clean and tops spring back when lightly touched, about 35 minutes. Let cool on a wire rack 10 minutes. Run a knife around edges of pans to loosen; invert to unmold. Remove parchment; reinvert onto racks. Let cool.

5. Using a long serrated knife, cut each cake in half horizontally. Place 1 bottom layer on a serving platter. Top with 1/3 of the apple mixture, spreading to edges. Stack 1 top layer on top of apples, and top with another 1/3 of the apple mixture. Repeat with remaining cake bottom and apples, and top with remaining cake top. Let stand at room temperature at least 1 hour before serving. Sift confectioners' sugar over top of cake.