Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and light brown sugar until light and fluffy, about 3 minutes.
Add the egg and vanilla extract to the butter and sugar mixture, and beat until fully combined.
In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Scoop tablespoon-sized portions of dough onto the prepared baking sheets, spacing them about 2 inches apart. Flatten each dough ball slightly with the back of a spoon or your fingers to encourage thinness.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are golden brown and the centers are set.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.