Preheat the oven to 350°F. Line 2 muffin tins with paper liners. (This recipe will make 20 cupcakes.)
To the bowl of a stand mixer, add the sugar, oil, vanilla, and eggs. Mix on medium-low speed until the mixture is light yellow, about 3 minutes.
In a separate bowl sift together flour, cinnamon, nutmeg, baking soda, and salt.
With the mixer on low speed, slowly and gently add in the dry ingredients. Mix until JUST combined.
Continuing to mix on low, add the nuts, carrots, and pineapple.
Scoop the batter into the lined muffin tin, filling each cup about ¾ of the way full.
Bake for 24 minutes, or until golden brown.
Transfer the muffin tins to a wire rack to cool for a few minutes before gently removing the cupcakes from the muffin tin to cool completely. While the muffins are cooling, make the frosting.