Preheat the oven to 350℉ (175℃). Set up the oven to bake in the bottom one-third. Grease the bottom of a springform pan —line with parchment paper.
Wash, core, and peel apples. You can either quarter the apples and then use a knife to slice the apples without slicing all the way through, OR you can slice the apples into wedges. Toss the apple slices in a little lemon juice and the cinnamon/sugar mixture. Set aside.
Use a mixer to cream butter and 1 ¼ cup of sugar until it's light and fluffy—about 5 minutes. Take your time on this step.
1 ½ sticks unsalted butter, 1 ¼ cup granulated sugar
Add the eggs to the butter/sugar mixture one at a time, mixing in each egg before adding the next—about 30 seconds.
3 eggs
Add the vanilla and the milk. Mix to Combine.
2 teaspoon vanilla, 3 tablespoons milk
Sift together baking powder, flour, and salt. Add the dry ingredients to the batter mixture. Mix until combined.
1 ½ cup cake flour, 2 teaspoons baking powder, ½ teaspoon salt
Pour the cake batter into the prepared pan (or a greased and floured cake pan if a spring-form pan is unavailable).
Place the apples into the cake batter.
Bake until the edges of the cake are golden brown—approximately 45 to 55 minutes. Test the cake's doneness with a skewer or a probe thermometer (205℉/96℃)
Remove the cake from the oven, cool it on a wire rack for about 20 minutes, and then remove it from the springform pan. Continue to cool until the cake is at room temperature.
Optional glaze: If desired, when the cake is still slightly warm, brush the top of the apples with warmed apricot jam. This step gives the cake a beautiful shine.
apricot jam
When the cake is completely cool, sprinkle the top of the cake with powdered sugar.