Line a cupcake pan with cupcake liners and heat the oven to 350. Spread the pecans on a parchment lined baking sheet and bake for 5-8 minutes until lightly toasted. Set aside to cool and chop into small pieces.
Heat the butter in a small sauce pan until foaming. Swirl and watch the butter until it begins to brown. Stir with a baking spatula, scraping the bottom until there are lot of golden bits floating. Do not burn.
Shred the carrots and set aside. In the bowl of a stand mixer with paddle, add the sugar, brown sugar, cinnamon, ginger, baking powder, salt, baking soda, nutmeg, cloves, vanilla and eggs. Mix on low until combined and then raise to medium and beat until light and fluffy, about 5-7 minutes.
Slowly drizzle in the browned butter while the mixer is on medium. In a bowl, whisk the AP and WW flour together. Reduce the mixer to low and add the flour. Mix only until it mostly comes together. Stop the mixer and fold in the pecans and carrots by hand, making sure all the flour is mixed in, but don't overmix it.
Using a large cookie scoop, scoop batter into your cupcake liners filling them about 3/4 of the way full. These rise a little but not drastically. Bake for 10 minutes, then rotate the pan and bake 10-15 more minutes until the centers have risen and a tooth pick inserted comes out clean. Check them every 5 minutes because you don't want to overbake them.
Place on a cooling rack to cool completely before you frost them.