Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, beat 3/4 cup dark brown sugar, 3/4 cup granulated sugar, and 3/4 cup salted butter with a hand mixer until light and fluffy, about 1–2 minutes.
Add 1 large egg, 2 teaspoons vanilla extract, and 1/2 cup finely shredded carrots. Mix until fully combined.
Add in 2 1/2 cups flour and mix until combined.
Scoop 1½-inch portions of dough onto prepared baking sheets, spacing cookies about 2 inches apart.
Bake for 15–17 minutes, or until cookies are set and lightly golden around the edges.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.