Preheat oven to 350°F (175°C). Line a 12-cup muffin pan with paper liners. If making more, prepare a second pan or bake in batches.

In a large bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger. Set aside.

In a separate large bowl, combine the granulated sugar and light brown sugar. Pour in the melted butter and vegetable oil, whisking until well combined.

Add the eggs one at a time to the sugar mixture, whisking well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the wet ingredients, mixing with a spatula until just combined. Be careful not to overmix.

Fold in the grated carrots and chopped pecans (if using) until evenly distributed throughout the batter.

Divide the batter evenly among the prepared cupcake liners, filling each about two-thirds full.

Bake for 18-22 minutes, or until a wooden skewer inserted into the center of a cupcake comes out clean.

Let the cupcakes cool in the muffin pan for 5 minutes, then transfer them to a wire rack to cool completely before frosting.

In a large bowl with an electric mixer, beat the softened cream cheese and softened butter together on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.

Reduce speed to low and gradually add the sifted powdered sugar, 1 cup at a time, until fully incorporated.

Add the vanilla extract and a pinch of salt. Beat on medium-high speed until the frosting is light and fluffy, about 2-3 minutes.

If the frosting is too thick, add milk or heavy cream 1 tablespoon at a time until desired consistency is reached.

Once the cupcakes are completely cooled, use a spatula or piping bag to frost each cupcake generously with the cream cheese frosting.

Garnish with a sprinkle of extra cinnamon or finely chopped pecans, if desired. Serve immediately or store.