To make the cupcakes:Heat oven to 350° F. Spread the pecans on a rimmed baking sheet and toast in oven, tossing once, until fragrant, 6 to 8 minutes. Let cool, then roughly chop.
Line a standard 12-cup muffin tin with paper liners. Whisk together the flour, cinnamon, salt, baking powder, baking soda, and nutmeg in a large bowl; set aside. In a medium bowl, whisk together the brown sugar, oil, and egg; fold in the carrots and ½ cup of the pecans. Add the carrot mixture to the flour mixture and mix until just combined and evenly moistened (do not overmix).
Divide the batter among the muffin cups and bake, rotating once, until a toothpick inserted in the center of a cupcake comes out clean, 20 to 25 minutes. Let cool slightly in the tin, then transfer to a wire rack to cool completely.
To make the frosting:Beat the cream cheese, butter, vanilla, and salt with an electric mixer on medium speed until smooth. Reduce mixer speed to low and gradually beat in the confectioners’ sugar, beating until smooth. Refrigerate the frosting until slightly stiffened, 20 to 30 minutes. Frost the cupcakes, dividing the frosting evenly, and top with the remaining ½ cup of pecans.