Preheat the oven to 350°F. Grease a 9" round cake pan. Add the melted butter to the pan, swirling to cover the entire bottom of the pan. Sprinkle the brown sugar evenly on top. Arrange a single layer of apple slices onto the melted butter and sugar mixture, and finish with the cinnamon. Set aside.
In a small bowl, whisk the flour, baking powder, salt, and baking soda together. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the sugar. Add the Greek yogurt, milk, and vanilla extract and mix until combined. Add the dry ingredients and mix on low speed until just combined. The batter will be thick.
Transfer the batter into the prepared pan, spreading evenly. Bake for 35-40 minutes or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool in the pan for 10 minutes. Use a knife to separate the sides of the cake from the pan, then invert cake onto a plate.
While you can use any type of apples here, I highly recommend Granny Smith.