Heat the oven to 350°F. Line two large baking sheets with parchment paper.
Whisk the flour, baking soda, baking powder, kosher salt, cinnamon, nutmeg, and ginger in a medium bowl.
In a large bowl, whisk the melted butter, brown sugar, and granulated sugar until smooth. Whisk in the egg and vanilla.
Stir in the grated carrots.
Add the dry mixture and stir just until no dry flour remains.
Scoop 2-tablespoon portions onto the prepared sheets, spacing them about 2 inches apart.
Bake 10 to 12 minutes, until the edges look set and the centers still look slightly soft.
Cool on the sheets for 5 minutes, then move to a wire rack and cool completely.