Preheat oven to 350°F (175°C). Grease and flour a 10-inch fluted tube pan.

In a large bowl, beat egg whites until foamy.

Gradually add 1 cup sugar, sour cream, applesauce, and vanilla extract. Beat until well combined.

In a separate bowl, combine flour, baking soda, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, beating until just combined.

In another large bowl, combine diced apples, chopped walnuts, 1/4 cup sugar, melted butter, and ground cinnamon.

Spoon half of the batter into the prepared tube pan.

Top with half of the apple filling.

Repeat the layers with the remaining batter and filling.

Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Cool in the pan for 10 minutes before inverting onto a wire rack to cool completely.

In a small bowl, combine confectioners' sugar, milk, and vanilla extract to make the glaze.

Drizzle the glaze over the cooled cake.