1/2 butter + more to grease pan
4 medium apples
1 tbsp ground cinnamon
1 cup + 1 tbsp sugar
1 cup all-purpose flour (unbleached is best)
1 egg, lightly beaten
1 1/2 cups coarsely chopped walnuts
Preheat oven to 350 degrees. Generously grease the bottom and sides of a 9-inch round cake pan with butter and set aside.
In a medium saucepan, over medium heat, melt the butter and set aside to cool to room temperature.
Peel, core, and cut the apples into 1/4" thick slices. Place the apple slices in a bowl with the cinnamon and 1 tablespoon of the sugar and toss to coat apples well. On the bottom of the prepared pan, place the apple slices in overlapping concentric circles. If necessary, make a second layer to use all the apple slices.
Into a large mixing bowl,sift the 1 cup of sugar and the flour. Using a wire whisk, whisk in the egg and melted butter just until mixed (DO NOT OVERMIX). Fold in the walnuts and mix in. Pour the batter evenly over the apple slices in the baking pan; smooth the top with a rubber spatula.
Place pan on the center oven rack and bake about 40 to 45 minutes or until the cake is golden brown and a wooden toothpick inserted in center comes out clean. Cool on a wire rack for 15 minutes or until the pan is cool. When pan is cool, run a knife around the edge and invert the cake on a serving plate. Serve warm or at room temperature, topped with whipped cream, if desired.