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 unsalted butter, granulated white sugar, and molasses. Whisk until smooth and well combined.
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 with a wooden spoon or spatula until just combined. Do not overmix.
Using a cookie scoop or tablespoon, 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 set but the centers still look slightly soft.
Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Store cooled cookies in an airtight container at room temperature.