Preheat oven to 425 F. Line a muffin tin with parchment paper and set aside.
Make wet batter: In a mixing bowl crack in the eggs, add brown sugar and mix for 1-2 min until well combined, add in the granulated sugar and mix for 1 min.
Add in butter and oil, whisk to combine. Add vanilla bean paste, sour cream and buttermilk. Mix until a smooth batter forms.
Make dry batter: In a separate bowl combine dry ingredients, all purpose flour, salt, cinnamon, baking soda, baking powder. Mix until well combined.
In a bowl add diced apples, add 2 tbsp dry batter in the apple and mix until completely coated.
Add dry mixture in the wet batter, add apples. Mix until just combined. Do not over mix at this point. Leave the batter at room temp undisturbed for 30-40 min.
Meanwhile prepare the caramelized apples. In a pan on medium heat, add butter, sugar, apple, corn starch, salt and cinnamon. Cook for 4-5 min stirring occasionally until apples are tender.
Make crumb coating by mixing melted butter, cinnamon, all purpose flour, cornstarch, sugar in a mixing bowl.
Make vanilla icing by mixing powdered sugar, milk, vanilla and salt in a bowl.
Pour batter in the prepared muffin tin, top them with caramelized apples and crumb topping.
