Preheat oven to 350 degrees. Use a muffin pan and spray with non-stick spray or use cupcake liners.
Mix brown sugar and cinnamon together in a bowl. Set aside.
In another medium-sized bowl, beat white sugar and butter together using an electric mixer until smooth and creamy.
Beat in eggs, 1 at a time, until blended in; add in vanilla extract.
Combine & whisk flour and baking powder together in another bowl and add into creamed butter mixture and stir until just blended.
Mix milk into batter until smooth.
In each muffin cup, fill each tin ½ full of the cake batter; add 1 tablespoon of the apple/sugar mixture on top. Add your brown sugar/cinnamon mixture that you prepared in the beginning and top each muffin again by sprinkling the brown/sugar/cinnamon mixture between the 12 muffins.Lightly pat apple mixture into batter.
Pour the remaining batter over each of the apple layers and spread out with a butter knife, then top each muffin with remaining apples. Lightly pat apples into batter again.
Option: Swirl brown sugar mixture through apples using knife or spoon.(I did this with the Apple Fritter Bread on the blog, but not these muffins.)
Bake in the preheated oven until a toothpick inserted in the center of the muffin comes out clean, approximately 20-25 minutes.
To make glaze, mix powdered sugar and milk or cream together until well mixed.
Let cool for about 15 minutes before drizzling with glaze.