Preheat oven to 350°F (175°C). Line a 12-cup muffin pan with paper liners.

In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, light brown sugar, baking soda, ground cinnamon, ground nutmeg, and salt. Make sure there are no brown sugar lumps.

In a separate medium bowl, whisk together the eggs, vegetable oil, buttermilk, and vanilla extract until well combined.

Pour the wet ingredients into the dry ingredients. Mix with a rubber spatula until just combined. Be careful not to overmix.

Gently fold in the grated carrots, chopped walnuts (if using), and orange zest until evenly distributed.

Divide the batter evenly among the 12 prepared cupcake liners, filling each about two-thirds full.

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

Remove the cupcakes from the oven and let them cool in the muffin pan for 5 minutes before transferring them to a wire rack to cool completely. Ensure they are fully cooled before frosting.

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

Gradually add the sifted powdered sugar, 1 cup at a time, beating on low speed until combined, then increasing to medium speed until smooth. Continue until all the sugar is incorporated.

Add the vanilla extract, lemon juice, and a pinch of salt. Beat on medium-high speed for another 1-2 minutes until the frosting is light and fluffy. If the frosting is too thick, add a tiny bit more lemon juice or milk (1/2 tsp at a time). If it's too thin, add more powdered sugar (1 tbsp at a time).

Once the cupcakes are completely cool, frost them generously with the cream cheese frosting. You can use an offset spatula or a piping bag with your favorite tip.

Optionally, garnish with a sprinkle of chopped walnuts or a tiny piece of carrot.

Serve immediately or store.