Preheat the oven to 350°F (175°C). Grease and flour a 9-inch (23 cm) round cake pan.
In a small bowl, toss the sliced apples with 2 tablespoons granulated sugar and 1 teaspoon ground cinnamon. Set aside.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the softened butter and 3/4 cup granulated sugar with an electric mixer until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Alternately add the flour mixture and milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared cake pan and spread evenly.
Arrange the cinnamon-sugar-coated apple slices neatly on top of the batter, slightly pressing them in.
Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.
Before serving, dust the top with powdered sugar.