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 unsalted butter until smooth.
Add the egg and vanilla extract to the sugar and butter mixture. 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 gently until just combined. Do not overmix.
Using a teaspoon or small cookie scoop, drop small rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart to allow spreading.
Gently flatten each dough ball 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.