Preheat Oven & Prepare Pan: Preheat your oven to 375°F (190°C). Line a standard 12-cup muffin tin with paper liners. If using nuts, toast them in the oven at 350°F (175°C) for about 10 minutes until fragrant; let cool before chopping.

Combine Dry Ingredients: In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, cardamom, and allspice. Set aside.

Mix Wet Ingredients: In a separate medium bowl, whisk together the vegetable oil, sour cream, applesauce, granulated sugar, brown sugar, eggs, and vanilla extract until smooth and well combined.

Blend Wet and Dry Mixtures: Pour the wet ingredients into the bowl with the dry ingredients. Stir gently with a spatula until almost fully incorporated. Add the grated carrots and toasted nuts (if using), folding them in until evenly distributed and no streaks of flour remain.

Fill Liners & Bake: Divide the batter evenly among the prepared cupcake liners, filling each about three-quarters full. Bake at 375°F (190°C) for 5 minutes, then reduce the oven temperature to 350°F (175°C) without opening the door and bake for an additional 12 minutes, or until the centers spring back when lightly touched.

Cool Cupcakes: Allow the cupcakes to cool in the pan for a few minutes, then transfer them to a wire rack to cool completely.

Prepare Frosting: In a mixing bowl, beat the softened cream cheese and butter together on medium speed until smooth, about 1 minute. Gradually add the sifted powdered sugar on low speed. Once combined, scrape down the sides of the bowl, add the vanilla extract and a pinch of salt, and beat on medium speed until light and fluffy.

Frost & Serve: Once the cupcakes are completely cool, frost them using a spatula or piping bag fitted with a decorative tip.

Storage: Store the frosted cupcakes in an airtight container in the refrigerator for up to 5 days.