Preheat the oven to 350°F. Line two large baking sheets with parchment paper and set aside.
In a medium bowl, whisk together flour, baking soda, baking powder, kosher salt, cinnamon, nutmeg, and ginger.
In a large bowl, whisk together melted butter, light brown sugar, and granulated sugar until smooth. Add the egg and vanilla extract, and whisk until fully combined.
Stir in the grated carrots.
Add the dry ingredients to the wet ingredients and mix just until no streaks of flour remain. Do not overmix.
Using a 2-tablespoon cookie scoop or spoon, portion the dough onto the prepared baking sheets, leaving about 2 inches of space between each cookie.
Bake for 10 to 12 minutes, or until the edges are set and the centers appear slightly underbaked.
Remove from the oven and let the cookies cool on the baking sheets for 5 minutes. Transfer them to a wire rack to cool completely before assembling.
While the cookies cool, make the sandwich filling.