Preheat your oven to 350°F (175°C) and grease a 9-inch round or square baking pan, lining it with parchment paper.
Peel, core, and thinly slice the apples, then set them aside.
Whisk together the flour, baking powder, baking soda, salt, ground cinnamon, and optional cardamom in a mixing bowl.
In another bowl, whisk together the cooled melted butter, granulated sugar, eggs, vanilla extract, and yogurt or sour cream until smooth.
Gradually add the dry ingredient mixture to the wet ingredients and stir just until combined.
Spread half of the batter into the prepared pan, arrange half of the apple slices on top, then dollop the remaining batter and place the rest of the apple slices on top.
Mix the extra sugar and ground cinnamon for topping, sprinkle over the apples, and bake for 40–45 minutes until golden brown.