Preheat your oven to 350°F (175°C) and line a large baking tray with parchment paper.
In a large bowl, cream together the softened butter, brown sugar, and granulated sugar using a mixer on medium speed until the mixture is light and fluffy, about 2 minutes.
Beat in the egg and vanilla extract until fully combined, scraping down the sides of the bowl as needed.
In a separate medium bowl, whisk together the flour, oats, cinnamon, ginger, nutmeg, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined.
Gently fold in the grated carrots and pecans using a spatula until evenly distributed.
Scoop rounded tablespoons of dough onto the prepared baking tray, spacing them about 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are lightly golden and the centers look set but soft.
Let the cookies cool on the tray for 5 minutes before transferring them to a wire rack to cool completely.
While the cookies cool, whisk together the cream cheese, powdered sugar, and milk until smooth, then drizzle over the cooled cookies.