Make the apple pie filling by adding the sliced apples, butter, brown sugar, cinnamon, nutmeg, and ginger to a saucepan and cooking over medium heat until the apples begin to soften.
Mix the cornstarch and water together to make a slurry, then stir it into the apple mixture and cook for 1–2 minutes, stirring constantly, until thickened.
Set aside to cool.
For the crumble, combine the flour, brown sugar, and granulated sugar, then cut in the cold cubed butter until coarse crumbs form.
For the muffin batter, whisk together the flour, baking powder, salt, and cinnamon.
In a separate bowl, cream the softened butter, granulated sugar, and brown sugar until light and fluffy, then beat in the eggs and vanilla.
Add the dry ingredients alternately with the milk, mixing just until combined, then fold in the chopped apples.
Fill a lined muffin pan with the batter, add some apple pie filling to each muffin, and generously top with the crumble.
Bake at 350°F (175°C) for 20–25 minutes, or until golden and a toothpick inserted into the muffin portion comes out clean.
Let the muffins cool, then drizzle generously with caramel sauce before serving.
