Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy.
Add eggs one at a time, mixing well after each. Stir in vanilla extract.
In a separate bowl, whisk together flour, baking powder, baking soda, cinnamon, ginger, and salt.
Gradually add dry ingredients to the wet mixture until just combined.
Fold in shredded carrots and pecans.
Scoop dough onto prepared baking sheets, spacing 2 inches apart.
Bake 12–14 minutes or until edges are golden. Cool completely.
For frosting: beat cream cheese and butter until smooth. Add powdered sugar and vanilla; beat until creamy.
Spread frosting over cooled cookies and serve.