Preheat your oven to 225°F.
Spread the pecans out on a baking sheet and roast in the preheated oven for 15 minutes. Remove from the oven and finely chop once cooled. (You can also use pre-chopped or pecan pieces)
Peel the carrots and grate using the large holes on a box grater.
Increase the oven temperature to 350°F. Line a 12-count muffin pan with cupcake liners and lightly spray the inside of each liner with non-stick spray.
In a medium bowl, whisk the flour, baking powder, salt, cinnamon, and ground nutmeg. In a larger bowl, whisk the vegetable oil, both sugars, room temperature eggs, vanilla extract, and sour cream. Scrape down the sides of the bowl with a rubber spatula as needed. Add the dry ingredients and whisk until smooth. Stir in the chopped pecans and the grated carrots.
Scoop the batter evenly into the cupcake liners, filling each about ¾ of the way up. Tap the pan on the counter a few times to release any trapped air bubbles.
Bake the cupcakes for 15-17 minutes. A toothpick inserted in the center should come out clean. Let cool in the pan and then cool completely in the fridge before frosting.