In a medium pot or skillet over low heat melt the butter then add the brown sugar, water and chopped apples, stir together and cook for about 3 minutes over medium/high heat just to melt the sugar, then lower to medium/low and cook for another 5-10 minutes. Add the cinnamon if using in the last two of minutes of cooking time. Stir often, apples should be tender but not mushy. Move to a clean bowl to cool before adding to the cake batter.
FOR THE CAKE
Pre-heat oven to 350F (180C). Grease and flour an 8 inch cake pan.
Whisk together the flour, salt, baking powder, baking soda and cinnamon. Set aside.
In a large bowl beat together the sugars, egg and egg yolk until light and fluffy, about 3-4 minutes, then add the yogurt and melted butter and beat together, 1 minute.
Add the flour mixture to the beaten egg mixture and beat until smooth, do not over beat. Gently fold in the caramelized apples then spoon into the prepared pan.Bake for approximately 30-40 minutes or until toothpick (in the cake part) comes out clean or a couple of crumbs are attached and let cool completely or eat warm. You can serve it with a scoop of vanilla ice cream or a light dusting of powdered sugar. Enjoy!
Notes
To make your own cake/pastry flour, for every cup of all purpose flour remove two tablespoons and replace with 2 tablespoons of corn starch. Sift together before using.The cake should be stored in an airtight container or a covered cake dish. It will keep at room temperature for approximately 1-2 days. If left longer it should be refrigerated, covered well. It will last 4-5 days in the fridge.The cake can also be frozen. Wrap the completely cooled cake tightly in plastic and place in a freezer safe bag or container. It will keep for up to three months in the freezer.