In a medium mixing bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, ginger, and 1/4 cup (30 grams) of the finely chopped walnuts. In a separate large bowl, whisk together the oil, brown sugar, and eggs until smooth and well combined. Stir in the applesauce, vanilla extract, and shredded carrots. Add the dry mixture into the wet ingredients and stir just until everything is incorporated—avoid overmixing.

Using a large cookie scoop or spoon, evenly divide the batter among the prepared muffin cups, filling each about 3/4 full to make 12 cupcakes. Bake for approximately 19 minutes, or until a toothpick inserted in the center comes out clean. Allow the cupcakes to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely before frosting.

In the bowl of a stand mixer fitted with the paddle attachment, add the butter and sifted powdered sugar. Start mixing on low speed, gradually increasing to medium-high to avoid a sugar cloud. Beat for about 3 minutes, until the mixture becomes smooth (don’t worry if it looks dry at first—it will come together). Scrape down the sides and bottom of the bowl, then add the softened cream cheese and beat on medium-high for about 1 minute, until light and fluffy. Add the vanilla extract and beat for another 30 seconds, ensuring everything is fully blended. Scrape the bowl again as needed.

Frost the completely cooled cupcakes with the cream cheese frosting and, if desired, sprinkle with the remaining chopped walnuts for garnish. Enjoy immediately or store in an airtight container in the refrigerator for up to 2 days.