Combine melted butter and cocoa powder in a large mixing bowl and stir until well combined.
Add sugars and stir well.
Add egg, egg yolk, and vanilla extract and stir.
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 with plastic wrap and chill in the refrigerator for 30 minutes. Meanwhile, preheat oven to 350F (175C) and line a baking sheet with parchment paper.
After ChillingOnce dough has chilled, scoop cookie dough by 2 tablespoon-sized scoop and roll between your palms to form a smooth ball. Place on prepared baking sheet, spacing cookies at least 2” (5cm) apart.
Bake in center rack of 350F (175C) preheated oven for 10-11 minutes. Within 1 minute of removing from the oven, gently flatten the surface of the cookie using a clean, flat surface (I use the bottom of a 1-cup measuring cup). This will give you a smooth/flat surface for the frosting. Allow to cool completely before decorating.
Mint FrostingPlace butter in a large mixing bowl and use an electric mixer to beat until smooth and creamy.
Gradually add sugar and stir on low-speed until well combined.
Add salt, vanilla extract, and peppermint extract. Stir well.
Add food coloring (if using) and stir until evenly incorporated.
GanacheCombine chocolate and heavy cream in a medium-sized microwave-safe bowl.
Microwave on high for 25 seconds. Stir well. Microwave for another 25 seconds and stir again until you have a smooth consistency. If chocolate is still not melted, continue to microwave in 10 second increments until smooth.
AssemblySpread or pipe frosting evenly over cooled cookies (I use a piping bag fitted with an open tip).
Use a spoon to drizzle or gently spread ganache over the frosting. Allow chocolate to set before enjoying.