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 3-4 minutes.
Add the egg and vanilla extract to the butter and sugar mixture and beat until fully combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop small amounts 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 10-12 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.
Store the cooled cookies in an airtight container at room temperature.