Preheat the oven to 350°F (175°C) and grease a 9-inch round cake pan.
Toss the sliced apples with the lemon juice and set aside.
In a large bowl, whisk together the flour, baking powder, salt, cinnamon, and nutmeg.
Cut the cold butter into the dry ingredients until the mixture resembles coarse crumbs.
Stir in the granulated sugar.
In another bowl, whisk together the eggs, milk, and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined.
Fold in most of the sliced apples, reserving a few for the top.
Spread the batter evenly into the prepared cake pan.
Arrange the remaining apple slices over the top.
Sprinkle with the coarse sugar.
Bake for 45–55 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 15 minutes before transferring to a wire rack.
Dust with powdered sugar if desired.
Serve warm or at room temperature, optionally with whipped cream, vanilla ice cream, or warm custard.
