To make the cake:
Adjust oven rack to middle position and preheat oven to 350F/180C.
Line muffin pan with paper liners.
In a large bowl, whisk together flour, baking powder, baking soda, salt, cinnamon; set aside.
In food processor fitted with the shredding disk or using the medium holes of a box grater, shred carrots (you should have about 3 cups); set aside. (make sure you use a full pound of carrots, weigh them after they’ve been trimed and peeled).
In the bowl of standing mixer fitted with paddle attachment (or in large bowl and using hand-held mixer), beat eggs and both the granulated and brown sugars together on medium-high speed until thoroughly combined, about 45 seconds. Reduce speed to medium and add oil in slow, steady stream while the mixer is still running. Increase speed to high and mix until mixture becomes lighter in color and almost frothy, about 45 seconds to 1 minute longer. Turn off mixer. Stir in the flour mixture by hand using a rubber spatula until just incorporated. Stir in the carrots and walnuts. Give the batter a final stir to make sure everything is thoroughly combined. Scoop the batter into the lined muffin cups until each is 3/4 full.
Bake until a toothpick or a skewer inserted into center of cake comes out mostly clean, 25-30 minutes, rotating the pans halfway through baking time. Remove to a wire rack and let cool completely before frosting.