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 combined and smooth.
Add the egg and vanilla extract to the sugar and butter mixture. Whisk until fully incorporated.
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, scoop small amounts of dough onto the prepared baking sheets, spacing them about 2 inches apart. Flatten each dough ball slightly with the back of the spoon or your fingers to encourage spreading.
Bake for 10 to 12 minutes, or until the edges are golden brown and the centers are set but still slightly soft.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. This helps them crisp up further.
Store the cooled cookies in an airtight container at room temperature for up to one week.