Preheat oven to 350 degrees.
In the bowl of a stand mixer, combine the butter, shortening and sugars. Beat well to combine, then scrape down the sides of the bowl and continue mixing until light and fluffy about 4 minutes.
Add the vanilla and orange extracts.
In a separate bowl, combine the flour, baking powder, ginger and salt.
On low speed, gradually add the flour mixture and mix just until combined.
Stir in the carrots and pecans.
Scoop the cookies out onto parchment lined baking sheets.
Bake for 18 minutes or until the cookies are set and slightly browned.
Cool completely before frosting.
While the cookies are cooling, make the cream cheese frosting.
In the bowl of a stand mixer, combine the butter and cream cheese. Beat well.
Add the vanilla extract.
With the mixer on low speed, gradually add the powdered sugar until fully combined.
Increase the speed of the mixer to medium and beat for a few more minutes until the frosting is light and fluffy.
Frost the cooled cookies with the icing. If desired, color some of the frosting green and orange and pipe carrot decorations on top. Or, garnish with a toasted pecan half.