1. Make the caramelized apples: Cook granulated sugar and water in a medium saucepan over medium-high heat, without stirring, until sugar caramelizes, about 4 minutes. Reduce heat to low. Stir in apples. Cook, covered, until softened, about 6 minutes. Slightly mash apples with a fork until broken down but still chunky. Continue to cook, uncovered, stirring, until liquid evaporates, about 5 minutes. Let cool completely.

2. Preheat oven to 350 degrees. Make the cake: Butter a 10-inch Bundt pan. Dust with flour, tapping out excess. Sift flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and 1 teaspoon salt into a medium bowl.

3. Beat butter and brown sugar with a mixer on high speed until pale and fluffy, about 4 minutes. Add eggs, 1 at a time. Reduce speed to low, and add flour mixture in 3 additions, alternating with milk, beginning and ending with flour. Mix in caramelized apples and the walnuts.

4. Transfer batter to pan. Bake until cake is deep golden brown and a toothpick inserted into the center comes out clean, about 50 minutes. Let cake cool in pan set on a wire rack for 10 minutes. Turn out cake onto rack, and let cool completely.

5. Once cake is cool, make the glaze: Whisk together confectioners' sugar and cider. Drizzle over top of cake, letting it drip down the sides.