Preheat oven to 300 degrees. In a stand mixer fitted with a paddle attachment, cream butter, sugar and brown sugar until light and fluffy (about 5 minutes).
In mixing bowl, combine all dry ingredients. Set aside.
Scrape down sides of bowl and beat an additional 5 minutes.
Combine vanilla, yogurt, and half & half. Set aside.
Add eggs one at time to mixing bowl. Beat until combined after each.
Add half wet ingredients, alternating with equal parts dry ingredients.
Stir in carrots.
Scoop into lined muffin cups—about ½ cup each.
Bake 15-20 minutes. Cupcakes should spring back when touched and are done when atoothpick inserted comes out clean.
Let cool. Top with cream cheese icing.