Beat first 6 ingredients in large bowl with mixer until well blended. Stir in apples; pour into a well greased and floured Bundt pan.
Bake 1 hour to 1 hour 5 min. or until toothpick inserted near center comes out clean. Cool in pan 15 min. Loosen cake from side of pan with knife (cake will probably stick some). Invert cake onto wire rack; gently remove pan. Cool cake completely.
When cake is cooled, beat cream cheese, butter and milk with electric mixer. Gradually mix in powdered sugar. Beat until smooth. Add vanilla and beat until incorporated.
With large spoon, spoon icing onto cake. Cover and refrigerate until ready to serve. Store in refrigerator.