Combine melted butter and cocoa powder in a large mixing bowl and stir until well-combined.
Add sugars, egg, egg yolk, and vanilla extract and stir well.
In a separate, medium-sized bowl, whisk together flour, baking powder, baking soda, and salt.
Gradually add dry ingredients to wet, stirring until completely combined.
Cover dough and chill in the refrigerator for 30 minutes. Meanwhile, preheat oven to 350F (175C).
Once oven is preheated and dough is chilled, scoop dough into ¼ cup-sized balls (for LARGE cookies) or 2 Tablespoon-sized balls (for smaller/classic-sized cookies). Roll between your palms to form a smooth round ball. Space cookies at least 2” apart on baking sheet.
Transfer to center rack of 350F (175C) oven and bake for 10-12 minutes (for large cookies) or 9-10 minutes (for smaller cookies). Within 1 minute of removing from the oven, use the clean, flat bottom of a 1-cup measuring cup (or glass, etc.) to gently flatten the surface of the cookie (you want a smooth flat surface for adding the peanut butter). Allow cookies to cool on baking sheet for at least 5 minutes before removing to cooling rack to cool completely before decorating.
Combine peanut butter and butter in a medium-large mixing bowl. Use an electric mixer to beat until smooth and creamy.
Stir in vanilla extract and salt until well combined.
Gradually add powdered sugar until completely combined and you have a smooth but stiff mixture.
Scoop dough by 2 ½ Tablespoon portions (for large cookies) or 1 ½ Tablespoon portions (for standard cookies) and roll into a smooth ball (see note). Use your hands to flatten the mixture into a disk and press gently onto the surface of a cookie (if it’s too sticky, just spread it on the cookie gently with an icing spatula). Repeat until all cookies have been covered.
Place chocolate in a heatproof bowl. Pour cream into a small saucepan and warm over medium-low heat until steaming. Pour evenly over the chocolate, cover with foil, and let sit for 5 minutes. Remove foil and whisk until smooth. If chocolate hasn’t completely melted, you can heat in the microwave in 10-second intervals until smooth.
Drizzle chocolate over cookies. Allow chocolate to harden before enjoying (you can speed this up by popping them in the fridge, but cookies taste best at room temp).