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Step 1
Peel and core apples; slice 1/2-inch thick. Set aside. Use some of the butter to grease an 8-inch springform cake pan. Dust with a little flour. Heat oven to 350 degrees.
Step 2
Sift or whisk flour with baking powder. Set aside. In the bowl of a standing mixer, beat granulated sugar with 3/4 cup (1 1/2 sticks) of the butter for several minutes, until light and fluffy. Beat in eggs, one at a time, then beat mixture about 3 minutes until creamy. Gradually add flour mixture in three batches, alternating with milk, mixing well after each addition. Transfer batter to pan.
Step 3
Arrange the apple slices on top of batter in tight overlapping concentric circles, gently pressing them in a bit. Scatter almonds on top. Dust with brown sugar and cinnamon. Dot with remaining butter. Place in the oven and bake about 1 hour, until a cake tester comes out clean, the top has browned and feels fairly firm to the touch.
Step 4
Allow to cool in the pan until just warm. Remove sides of pan and serve with whipped cream or ice cream. If cake has cooled completely it can be warmed before serving.