Preheat oven to 350℉ degrees. Place liners in a cupcake tin and set aside.
In a large size bowl combine the wet ingredients: eggs, greek yogurt, vegetable oil, sugars, and vanilla extract. Stir until completely combined.
In a separate medium size bowl combine the dry ingredients: flour, baking powder, salt, nutmeg and cinnamon. Whisk together to combine.
Slowly add the dry ingredients to the wet and stir until mostly combined. Fold in the grated carrots and the chopped pecans. Don't overmix.
Scoop the batter and fill the cupcake liners about 3/4 full.
Bake for approximately 20 minutes, until a toothpick inserted in the center comes out clean.
Carefully remove the cupcakes from the tin and allow the cupcakes to cool on a wire rack.
To prepare the frosting add the cream cheese and butter to a mixing bowl. Mix until smooth. Add in the vanilla and powdered sugar. Mix on high speed until frosting is smooth and creamy.
Spread onto cooled cupcakes with an offset spatula or I used an Ateco 808 tip in a pastry bag.