Preheat the oven to 350°F (175°C). 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 and cooled unsalted butter, granulated white sugar, and molasses. Mix well until smooth.
Add the egg, egg yolk, and vanilla extract to the butter mixture. Whisk until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop dough balls 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 from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.