Line the muffin cups with cupcake liners. Preheat the oven to 350°F (175°C).
In a small bowl, combined together flour, baking powder, cinnamon, baking soda, salt and nutmeg. Set aside.
In a mixing bowl with a paddle attachment, mix together eggs, Greek yogurt, oil, sugar and brown sugar until well combined. Add flour mixture and mix just until combined. Don’t over mix at this point. Fold in grated carrots and pecans. Fill the cupcake cups ¾ of the way. Bake for 18-20 minutes, or until inserted toothpick comes out clean. Cool for 5 minutes in the baking pan, then transfer onto wire rack to cool completely.
To make the frosting, beat butter and cream cheese on medium high speed until fluffy for 1 minute. Add powdered sugar, heavy cream and vanilla extract. Beat on low speed for a minute. Then increase the speed to medium high and continue to beat until smooth and fluffy, about 3 minutes.
Frost the cupcakes once they’re completely cooled.