Preheat oven to 350°. In a small bowl, beat cream cheese and 1/4 cup sugar until smooth. Beat in 1 egg; set aside.
In a large bowl, beat oil with remaining sugar and eggs until well blended. Combine flour, baking powder, cinnamon, salt and baking soda; gradually beat into oil mixture until blended. Stir in apples, carrots and pecans.
Transfer half of the apple batter to a greased and floured 10-in. fluted tube pan; layer with cream cheese mixture and remaining apple batter.
Bake at for 50-60 minutes or until a toothpick inserted near the center comes out clean. Cool 10 minutes before removing from pan to a wire rack to cool completely.
In a large saucepan, bring the brown sugar, butter and milk to a boil. Cook and stir 1 minute. Remove from heat; whisk in confectioners' sugar and vanilla until smooth. Drizzle over cake. Sprinkle with pecans. Yield: 12 servings.