Preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper.
In a large mixing bowl with a hand mixer, beat the softened butter, granulated sugar, and brown sugar until smooth and glossy.
Add the egg, egg yolk, and vanilla. Mix until fully combined.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
Add the dry ingredients to the wet mixture and fold gently with a spatula just until combined. The dough will be thick and soft.
Scoop 2½–3 tablespoons of dough per cookie and roll into balls. Flatten into a 1 inch tall disc. Place them 3 inches apart.
Bake for 11-13 minutes, until the edges are set but the centers still look soft.
While the cookies are still warm, gently press the centers down with the back of a spoon or glass to create a shallow well.
Let cool completely on the baking sheet.