2 tablespoons butter, melted
5 1/2 cups granulated sugar
1/2 teaspoon ground cinnamon
1/2 teaspoon freshly-grated nutmeg
1 1/2 cups all-purpose flour
3 tart apples such as Granny Smith,
    peeled, halved, and sliced (3 cups)
1/2 cup butter
2 large eggs
1/3 cup milk
2 tablespoons rum
2 teaspoons vanilla extract
2 tablespoons finely chopped pecans
1 1/2 teaspoons baking powder
1 1/2 teaspoons baking soda
1 1/2 teaspoons salt

Preheat the oven to 350 degrees F. Brush the sides of an 8 x 3 1/4-inch spring-form pan with the melted butter.

Mix together 1/2 cup sugar, cinnamon, nutmeg and 1/4 cup flour and sprinkle the mixture evenly over the bottom of the pan.

Wrap foil around the pan to prevent leakage. Starting at the outside edge, arrange a ring of apple slices in the pan, slightly overlapping and pointing to the center. (It will feel backwards.) Fill in the center with another circle of apples, with some overlap occurring. Layer any remaining apple slices evenly, overlapping to prevent the batter from escaping.

With a wooden spoon or electric mixer, beat together the butter and 1 cup sugar. Add the eggs, milk, rum, and vanilla extract. The batter will look curdled. Add 1 1/4 cups flour, the nuts, baking powder, baking soda, and salt, beating only until the flour is completely incorporated. Pour the batter over the apples and spread evenly.

Place the pan on a baking sheet and bake in the middle of the oven until a wooden pick inserted in the cake comes out clean, about 70 minutes. Cover with a piece of foil if the top begins to brown too quickly.

Let the cake rest in the pan on a rack for 5 minutes, then, using a small, flexible knife, gently separate the sides of the cake from the pan. Invert the cake on the rack, letting it stay in the pan for another 10 minutes, then remove the pan, lifting it up carefully.