Preheat oven to 350 degrees F. (reduce temperature to 325 degrees F if your pan is dark/non-stick). Grease and flour a standard Bundt pan (12-cup capacity); set aside.
Make the Cream Cheese Filling: Beat the cream cheese, butter and sugar on medium speed until well combined and smooth. Add the egg, flour and vanilla and continue beating just until incorporated. Set aside.
Make the Apple-Pecan Cake: In a large bowl, whisk together the flour, both sugars, the cinnamon, nutmeg, allspice, baking soda and salt. In a separate medium bowl, whisk together the eggs, oil, applesauce and vanilla extract. Pour the egg mixture into the flour mixture and gently mix to combine using a whisk or rubber spatula.
Gently fold in the pecans and chopped apples until evenly distributed throughout the batter.
Spoon about 2/3 of the cake batter into the prepared pan. Top evenly with the cream cheese filling, leaving a 1-inch border around the edge of the pan. Use a thin paring knife to gently swirl the cream cheese filling with the cake batter just a few times – less is more. Spoon the remainder of the cake batter on top of the cream cheese filling and gently spread to the edges of the pan, covering the filling.
Bake for 60 to 75 minutes, or until a thin knife inserted in the center of the cake comes out clean. Transfer the pan to a wire rack and cool for 15 minutes, then invert the cake onto the rack and allow to cool completely (at least 2 hours).
Make the Praline Frosting: Combine the brown sugar, butter and milk in a 2-quart saucepan over medium heat. Bring to a boil, whisking constantly. Boil for 1 minute, continuing to whisk constantly, then remove the pan from the heat and stir in the vanilla. Gradually whisk in the powdered sugar until it is completely incorporated and the frosting is smooth.
Slowly pour the frosting over the cooled cake and garnish with extra pecans. Give the frosting 5 minutes to set, then serve. Store leftovers in an airtight container or wrapped tightly with plastic wrap at room temperature or in the refrigerator.