Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, whisk together the granulated sugar and melted butter until smooth.
Add the egg and vanilla extract to the sugar and butter mixture and whisk until fully combined.
In a separate bowl, sift together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Scoop about 1 tablespoon of dough per cookie onto the prepared baking sheets, spacing them at least 2 inches apart to allow for spreading.
Using the back of a spoon or your fingers, gently flatten each cookie dough ball to about 1/4 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 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 for up to 1 week.