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1
Preheat the oven to 350F.
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2
Brush the sides of a 8x3-1/4-inch springform pan with the melted butter.
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3
Mix together 1/2 cup sugar, cinnamon, nutmeg, and 1/4 cup flour and sprinkle the mixture evenly over the bottom of the pan.
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4
Wrap foil around the pan to prevent leakage.
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5
Starting at the outside edge, arrange a ring of apple slices in the pan, slightly overlapping and pointing to the center.
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6
(It will feel backwards.)
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7
Fill in the center with another circle of apples, with some overlap occurring.
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8
Layer any remaining apple slices evenly, overlapping to prevent the batter from escaping.
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9
With a wooden spoon or electric mixer, beat together the butter and 1 cup sugar.
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10
Add the eggs, milk, rum, and vanilla.
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11
The batter will look curdled.
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12
Add 1-1/4 cups flour, the nuts, baking powder, baking soda, and salt, beating only until the flour is completely incorporated.
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13
Pour the batter over the apples and spread evenly.
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14
Place the pan on a baking sheet and bake in the middle of the oven until a toothpick inserted in the cake comes out clean, about 70 minutes.
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15
Cover with a piece of foil if the top begins to brown too quickly.
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16
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.
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17
Invert the cake on the rack, letting it stay in the pan for another 10 minutes, then remove the pan, lifting it up carefully.
