Preheat your oven to 350 degrees
Prepare your cupcake tin by buttering or lining the cups and set aside for now
In a large bowl, combine 1/2 cup of vegetable oil, 2/3 cups of brown sugar, 1/3 cup of granulated sugar, 1/4 cup of unsweetened apple sauce, 2 large eggs and 1 teaspoon of vanilla extract until smooth
In a separate bowl, whisk 1 1/4 cups of all purpose flour, 1 teaspoon of baking powder, 1/2 teaspoon of baking soda, 1/4 teaspoon of salt, 1 teaspoon of ground cinnamon, 1/2 teaspoon of ground ginger, 1/4 teaspoon of all spice, 1/8 teaspoon of ground nutmeg, a pinch of black pepper and a pinch of cardamom until fully incorporated
Add the dry ingredients to the wet ingredients and mix until just combined
Fold the grated carrots and finely chopped nuts into the batter
Divide the batter between 12 cupcake tins (each tin should be around 3/4 of the way full)
Bake in a 350 degree oven for around 16 minutes or until they are lightly golden and a toothpick will come out of the center of a cupcake clean
Transfer the pan onto a cooling rack and once the cupcakes are cool enough to touch, transfer them directly onto the cooling rack
Make the cream cheese frosting by whipping 8 ounces of room temperature cream cheese with 1/4 cup of room temperature butter until combined
Gradually add 2 cups of sifted confectioners sugar and 1 teaspoon of vanilla extract and beat until smooth and creamy
Frost fully cooled cupcakes generously with cream cheese frosting
Garnish with additional finely chopped walnuts (optional)
Store in an airtight container at room temperature or the refrigerator