Preheat oven to 425°F and line a muffin pan with 12 cupcake liners.
In a medium bowl, mix together flour, brown sugar, granulated sugar, nutmeg, cinnamon, and salt. Cut in the cold butter with a pastry cutter or food processor until pea-sized crumbles form.
In a large bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt. Set aside.
In another bowl, beat together softened butter and both sugars until smooth and creamy. Add eggs, yogurt, and vanilla extract, and beat until combined.
Slowly mix in the dry ingredients and milk. Fold in chopped apples.
Fill each muffin liner with batter, then sprinkle crumb topping on each muffin and press it down gently.
Bake muffins for 5 minutes at 425°F, then reduce heat to 350°F and bake for another 15-20 minutes until a toothpick comes out clean.
Let muffins cool for 5-10 minutes before transferring to a wire rack to continue cooling.
In a separate bowl, cream together softened butter, cream cheese, powdered sugar, and vanilla extract until smooth. Load mixture into a piping bag and drizzle over muffins while they are still warm.
Enjoy your delicious Apple Cinnamon Streusel Muffins!