Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, combine the melted butter, granulated white sugar, and molasses. Mix until smooth and well combined.
Add the egg, egg yolk, and vanilla extract to the butter mixture. Beat until light and creamy, about 2 minutes.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers still look soft.
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.