Preheat oven to 350 °F (177 °C). Line two baking sheets with parchment paper or silicone baking sheets. Place granulated sugar in a shallow dish and set aside. Combine flour, cocoa, baking soda, and baking powder in a bowl. Whisk to combine.
Microwave 10 tbsp. butter, covered, in a large bowl until melted, about 1 minute. Remove from microwave and stir in remaining 4 tbsp. of butter until melted. Allow butter to cool to 90-95 degrees, about 5 minutes.
In the bowl of a stand mixer with the paddle attachment, mix brown sugar, vanilla, salt, and melted butter together until no lumps remain. Add in the egg and yolk and mix until smooth. Gently add in the flour mixture and mix until just combined.
Working with 2 tbsp. of dough at a time, roll balls in granulated sugar and divide between baking sheets. Using a bottom of a drinking glass, flatten cookies to 2 inches in diameter. Sprinkle each sheet of cookies with 1 1/2 tsp. remaining granulated sugar.
Bake 1 sheet at a time until cookies are slightly puffy and edges have begun to set, about 15 minutes, rotating sheet halfway through baking (cookies will look slightly underdone between cracks). Let cookies cool on sheets for 5 minutes, then transfer to wire rack. Let cookies cool completely before serving.