Place flour, granulated sugar, brown sugar, cinnamon, nutmeg, allspice, salt and baking soda in bowl of an electric stand mixer outfitted with a paddle attachment. Stir at low speed to combine. Add the eggs, oil, applesauce and vanilla to the bowl, and mix at medium speed until dry ingredients are just moistened. Stir in the chopped apples and walnuts.
Preheat oven to 350.
Grease and flour a 14-cup Bundt pan. Pour half of the apple batter into the pan, using a spatula to spread evenly over the bottom of the pan. Spoon the cream cheese mixture over the batter, leaving a 1-inch border around edges of pan. Spread the remaining batter over the cream cheese mixture, making sure the batter extends all the way to the outer edges of the pan. (This will prevent the cream cheese filling from oozing out at the cake cooks.)
Place pan in preheated oven and bake for 60-70 minutes, or until a tester inserted into the cake comes out clean. (Be sure when testing to not insert the tester through the cream cheese filling, as this might make the cake appear uncooked.) Cool in pan on wire rack for 10-15 minutes before inverting onto the rack to cool completely.