1. Preheat oven to 350°F. Prepare a muffin pan with non-stick spray or liners.

2. Mix brown sugar and cinnamon together in a small bowl; set aside.

3. Beat granulated sugar and butter until creamy. Add eggs one at a time, then mix in vanilla extract.

4. Combine flour and baking powder in a separate bowl, then mix into the creamed butter mixture. Stir in milk until smooth.

5. Toss chopped apples with 2 tablespoons granulated sugar and 1 teaspoon cinnamon.

6. Fill muffin cups halfway with batter.

7. Top with some of the apple mixture and sprinkle with the brown sugar-cinnamon mixture. Lightly pat into the batter.

8. Add the remaining batter over the apples, spreading evenly.

9. Top with the remaining apples and lightly pat them into the batter.

10. If desired, swirl the brown sugar mixture through the apples and batter using a knife or spoon.

11. Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.

12. Mix powdered sugar with milk or cream to create the glaze.

13. Cool muffins for 15 minutes, then drizzle with the glaze before serving.