Add ¼ cup butter to a 9-inch round cake pan or springform pan. Place in the oven for a few minutes until the butter has melted.
Sprinkle brown sugar over the melted butter in the bottom of the pan.
Cut the apples into half circles about ¼-inch thick* (no need to peel!) and arrange them in concentric circles on top of the brown sugar, overlapping them slightly until they fill the entire bottom of the pan. Set aside.
Add flour, sugar, baking powder, ground cinnamon, and salt to a large bowl. Whisk to combine.
Add milk, remaining 1/4 cup melted butter, vanilla, and egg. Whisk again until just combined.
Pour batter over apple slices, smoothing from edge to edge, as needed.
Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Run a knife around the edge of the pan. Let cool to room temperature before flipping onto a serving plate.
Notes
Butter: Feel free to substitute salted butter for the unsalted butter and omit the salt.
Dark brown sugar: You can substitute dark brown sugar for the light brown sugar if you prefer.
Apples: Any baking apple will work in this recipe. Granny Smith will give you tarter topping, and Pink Lady will give you sweeter topping.
Flour: Weighing the flour is the most accurate way to measure it (click on "metric" just above the ingredients for the weights). You can also sift or stir the flour, lightly spoon it into the measuring up, and level.
Cinnamon: You could substitute apple pie spice for the cinnamon.
Milk: Any milk from whole milk to skim milk will work. Whole milk will give you moister, richer cake than using skim milk. Plant based milk, like almond milk, also works.