Preheat the oven to 350 degrees F. Spray a 9x13 inch baking pan with nonstick baking spray.
Toast the nuts for the frosting first. Spread the pecans out on a baking sheet. Place in the oven for 8 to 20 minutes, until golden and toasty and fragrant. Remove and let them cool, then chop.
In a small bowl, whisk together the flour, baking soda, cinnamon, salt, nutmeg and baking powder.
In a large bowl, whisk together the sugar and the eggs until smooth. Whisk in the oil and greek yogurt. Whisk in the vanilla extract.
Stir in the dry ingredients until just combined. Fold the carrots in with a spatula until they are evenly dispersed.
Spread the batter in the greased baking pan.
Bake for 35 to 40 minutes, or until a tester inserted into the center comes out clean. Let cool completely before frosting.