Start by browning the butter. You'll take ½ cup of butter (one stick) and melt in a medium saucepan, and then continue to cook past the point of boiling. You will do this over low-medium heat, past the point of the butter foaming, until it turns a nice golden brown, and has a nutty smell. Make sure you are stirring and watching it, because it will turn from perfectly brown to burnt fairly quickly. Once finished browning, pour all of it into a bowl and allow to cool completely.
Preheat the oven to 325 degrees. Spray and line an 8 or 9 inch pan with cooking spray and parchment paper.
In a small bowl whisk together the flour, baking powder, salt, cinnamon, nutmeg, ginger and all spice. Set aside.
In a large bowl whisk together the browned butter, both sugars, eggs and vanilla until light and fluffy, about 2-3 minutes.
Add half of the dry ingredients to the wet ingredients, whisking until combined. Add the buttermilk, followed by the remaining dry ingredients.
Using a box grater, grate your apple on the large side. Or you can dice the apple into very small squares if preferred. Fold apples into the cake batter.
Pour batter into prepared cake pan and smooth out the top. Sprinkle the top of the cake with cinnamon and sugar.
Bake cake for 33-37 minutes, or until the edges pull away from the pan, and have a golden brown edge. The top will develop a hard shell from the cinnamon and sugar, but you can stick a toothpick through if you want to test it that way. Allow to cool before serving.