Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together flour, baking soda, salt, cinnamon, and ginger.

In a large bowl, cream together 1/2 cup butter, brown sugar, and granulated sugar until light and fluffy.

Beat in the egg and 1/2 teaspoon vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the grated carrots, pecans, and raisins using a spatula.

Drop rounded tablespoons of dough onto the prepared baking sheets, spaced 2 inches apart.

Bake for 10 to 12 minutes or until the edges are lightly browned and the centers are set.

Transfer cookies to a wire rack and allow to cool completely.

In a separate bowl, beat cream cheese and 2 tablespoons butter until smooth.

Gradually add powdered sugar and 1/2 teaspoon vanilla extract to the cream cheese mixture, beating until creamy.

Frost the cooled cookies with the cream cheese mixture before serving.