Add all ingredients to a medium saucepan over medium heat. Bring to a boil and slightly reduce heat. Let the mixture simmer, stirring occasionally, until apples are soft. Mash apples and continue to cook until mixture has thickened. It should be the consistency of really thick applesauce, and be able to coat the back of a wooden spoon or rubber spatula. (It's okay if it's lumpy!) Remove from heat and let cool.

Stir together all ingredients and transfer to a squeeze bottle or piping bag. Set aside.

Preheat oven to 350 degrees and spray a 9 or 10-inch springform pan with cooking spray.

Whisk together flour baking powder, baking soda, salt, and cinnamon in a bowl and set aside.

Beat butter on medium-high speed with an electric mixer until smooth and creamy. Add sugar and mix until fluffy. Add eggs and mix well. Then add flour mixture and milk; mix until combined. Add apple butter and mix until incorporated.

Pour batter into the prepared springform pan, and place the pan on a baking sheet. Using the squeeze bottle or piping bag, pipe a spiral of cinnamon filling on the top of the cake. (I piped a thin spiral first, and then went back and make it thicker.)

Bake for 40-45 minutes, or until center has set and a toothpick inserted into the center of the cake (not the cinnamon part) comes out clean. Let the cake cool for 10-15 minutes.

Whisk together all ingredients until smooth. Drizzle over cake and serve!