Preheat oven to 350°F and grease a 10-inch bundt pan. Set aside.
In a large bowl, combine the brown sugar, canola oil, applesauce, vanilla and orange zest and whisk until no lumps remain. Add eggs, one at a time, whisking until incorporated after each addition. Set bowl aside. In another large bowl, combine the dry ingredients: flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg and cloves and whisk until combined. Pour the dry ingredients into the wet ingredients and fold until just combined. Then fold in the carrots, raisins and pecans if using. Spread half of the batter into the bottom of the prepared bundt pan.
In the bowl of a stand mixer, or in a medium bowl using a hand-held mixer, beat the cream cheese until light and creamy, 1-2 minutes. Add the sugar and vanilla and beat on high speed until fully incorporated. Then add the egg and mix until just incorporated. Spread this cheesecake layer over the carrot cake layer. It will start to drop into the carrot cake batter – but that’s ok! It is a carrot-cheesecake swirl after all! After adding the cheesecake layer, spread the remaining carrot cake batter over the cheesecake and gently smooth.
Bake for 55-75 minutes until a toothpick inserted comes out clean. If the top of the cake starts to brown before the inside is done, lightly cover with aluminum foil and continue to bake. Once the cake is done, remove from the oven and allow to cool in the pan for 30 minutes. After 30 minutes, invert onto a wire rack and allow to cool completely.
While the cake is cooling make the frosting. In a microwave safe bowl, heat the cream cheese for 20 seconds or so until it is just soft enough to whisk. Whisk until somewhat smooth and then add the powdered sugar, salt, vanilla and cinnamon and whisk again until smooth. Add milk or cream to the cream cheese starting with 2 tablespoons and adding more depending on your desired consistency. For a thinner, glaze like mixture add more. For a thicker, spreadable mixture use less! Pour or spread on top of the cake once cool. Serve and enjoy!