Preheat oven to 375°F. Line a 12-cup muffin pan with muffin liners.
In a medium sized bowl mix flour, baking powder, baking soda and salt. Set aside.
In a large bowl beat together butter, 1 cup granulated sugar and eggs until smooth, then mix in vanilla extract. Stir in apples and walnuts
Gradually add the flour mixture to the wet ingredients and mix until combined. Set aside until ready to assemble.
Cream Cheese Center
Beat together cream cheese, 1/4 cup granulated sugar and egg yolk until smooth. Set aside until ready to assemble.
Crumb Topping
Add the brown sugar, cinnamon and butter to a small bowl and mix with a fork. Add the flour and continue to mix until it starts to become a crumb-like texture.
Assembly
Add 1 tablespoon of the batter into the bottom of each of the muffin liners.
Layer 1 tablespoon of the cream cheese mixture on top of the muffin batter in each of the muffin liners.
Add another layer of muffin batter to the tops of the the cream cheese layer fill to the tops of each of the muffin liners.
Top each of the muffins with the crumb mixture and lightly press into the top. Bake for 20 minutes or until the tops are lightly brown. Let them sit for 5 minutes and then remove to a wire rack to cool.
