Preheat oven to 400 degrees. Line nine muffin cups with cupcake liners.
For the apples - In a skillet, cook apples, butter, cinnamon, brown sugar, and water. Cook over medium heat for about 5 minutes or until tender. Remove from heat. Sprinkle with flour and toss to coat.
For the muffins - In a bowl, add the flour, baking powder, baking soda, cinnamon, and salt. Whisk together.
Add in the remaining muffin ingredients. Stir together just until combined. Then fold in the apple mixture. Filled lined muffin cups with batter. Each one should be full of batter.
Bake at 400 degrees for 15-17 minutes until a toothpick inserted in the center comes out clean. Allow to cool. Once cooled, prepare the glaze.
In a bowl, combine the powdered sugar vanilla and enough milk to make a thick glaze. Dip the top of each muffin in the glaze and allow to sit 5 minutes. You can re-dip the muffins if desired for a thicker glaze. Makes 9 muffins.