Preheat your oven to 180°C (350°F). Line a muffin tin with cupcake liners or lightly grease the cups.
Peel and finely grate the carrots. Set aside.
In a large bowl, beat the eggs and brown sugar together using a hand mixer or whisk until the mixture is pale, light, and fluffy — this should take about 2–3 minutes. Gradually add the oil while mixing, then stir in the grated carrots.
In a separate bowl, sift together the flour, baking powder, baking soda, and cinnamon. This ensures even distribution and prevents lumps.
Gently fold the dry ingredients into the wet mixture until just combined. Then stir in the chopped walnuts and freshly grated orange zest.
Divide the batter evenly among the cupcake liners. Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean. Allow the cupcakes to cool completely on a wire rack.