Grease and flour a 14-cup Bundt pan. Beat the cream cheese, softened butter and sugar until smooth. Add the filling egg, flour and vanilla and beat just until combined. Set aside.

Heat the oven to 350°F. Bake the cake pecans for 5 to 7 minutes, until lightly toasted and fragrant.

Stir the cake flour, both cake sugars, salt, baking soda and spices together in a large bowl. Stir in the beaten eggs, then the oil, applesauce and vanilla. Stir in the chopped apples and toasted pecans.

Spoon two-thirds of the apple batter into the pan. Spoon the cream cheese filling over it, leaving a 1-inch border around the edges of the pan. Cover with the remaining apple batter.

Bake at 350°F for 1 hour to 1 hour and 15 minutes, until a long wooden skewer inserted in the center comes out clean. Cool in the pan on a wire rack for about 1 hour, then remove the cake from the pan and cool completely before frosting. Refrigerate the cake before it has spent more than 2 hours at room temperature.

Once the cake is completely cool, bring the frosting brown sugar, butter and milk to a boil in a saucepan. Boil for 1 minute. Remove from the heat, add the vanilla, then whisk in the powdered sugar until fully combined. Let cool slightly, about 5 minutes, until thickened but still pourable. Pour over the cake and garnish with the optional pecans.