Preheat the oven to 350F. Take out a 9-inch cake pan and lightly grease.
In a skillet, heat half the butter until melted and slightly bubbly. Add one cup of the sugar and cook until a caramel brown color. Add in half the cinnamon and vanilla extract and stir well.
Pour the caramel mixture into the baking pan and make sure it is spread evenly on the bottom.
Place the apple slices onto your baking pan over the caramel. They should be fairly close together, but not too tight. You might not need to use all of the apple slices, depending on the size of your apples. That's okay. They make a good snack while your cake is baking.
In a small bowl, mix together the flour, baking powder, baking soda, remaining cinnamon, ginger, cardamom and salt together. Set aside.
In a separate bowl cream the remaining butter and sugar together until light and fluffy. Add the eggs one at a time and beat well between each egg. Add in the remaining vanilla and the yogurt.
Pour the flour mixture into the wet ingredients and mix until combined. the batter should be quite thick.
Pour the cake batter over the apples and spread to the edges. Since the batter is so thick, it will take some gentle coaxing to get the batter to spread evenly. You don't want to work it too hard otherwise the apple slices will start moving around.
Bake for about 30 - 35 minutes, or until a toothpick comes out clean. Allow to cool for 10 minutes. Run a knife along the edges of the cake, then place a plate over the pan and carefully, but quickly turn over the pan and plate so that the pan is on top. Carefully remove the pan and the cake should come out easily. Wait 10 minutes before slicing.