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 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, scoop out dough and place on the prepared baking sheets, spacing them about 2 inches apart. Flatten each dough ball gently with the back of a spoon or your fingers to about 1/8 inch thickness.
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 sheet for 5 minutes before transferring to a wire rack to cool completely.
Store the cookies in an airtight container at room temperature for up to 1 week.