Preheat the oven to 375°F. Grease a 9-inch square baking dish with or pie pan with a 4-cup capacity.
In a medium bowl, whisk vigorously together the flour, baking powder, and salt.
In a separate small bowl, mix 1/4 a cup of the sugar with the cinnamon, set aside.
Using an electric mixer, beat the butter with the remaining 1/4 cup sugar. Beat in the egg until blended. Add the flour mixture in three additions, alternating with the milk, beating after each addition until just combined.
Pour half of the batter in the bottom of the baking dish. Lay the apple slices on the batter so they just cover the batter (you may have to overlap some slices). Sprinkle the apples with the cinnamon-sugar mixture, reserving a teaspoon or two to sprinkle on top. Spread the rest of the batter over the apples. Sprinkle the remaining cinnamon-sugar on top.
Bake the cake for 25 minutes or until it is golden brown and apples start to bubble at the edges.