Preheat Oven: 350
Line muffin tin with cupcake liners
In a medium bowl, whisk together flour, baking powder, baking soda, salt and cinnamon; set aside
Using the smallest holes (less than 1/4-inch in diameter) of a box grater or food processor, grate the carrots to yield 1 3/4 cups
Place carrots, eggs, buttermilk, vanilla, sugar, olive oil, butter, and ginger in a large bowl; whisk until well combined
Using a rubber spatula, fold the dry ingredients into the carrot mixture until just combined
Fill each paper liner with batter; filling to the top
This will make 12-14 cupcakes
Bake 20-25 minutes
Let cool in pan for 10 minutes
Remove to cooling rack to cool completely
For the frosting, in a bowl of an electric mixer fitted with a paddle attachment, beat butter on medium-high speed until fluffy; about 2 minutes
Add the cream cheese and confectioner's sugar; beat until combined and fluffy;
about 2 minutes
Add the orange zest, ginger and salt; beat 5 minutes