In a large mixing bowl, whisk together the melted butter and cocoa powder.
Add the brown sugar and granulated sugar and beat with an electric mixer on medium speed until well combined.
Add the eggs and vanilla extract and beat on medium speed until incorporated.
In a medium mixing bowl, whisk together the flour, baking soda, and salt. Stir the mixture into the wet ingredients.
Cover the bowl with a lid or plastic wrap and refrigerate for 45 minutes.
While the dough is chilling, preheat the oven to 350F.
Roll the dough into 1.5-inch cookie dough balls and place on a ungreased baking sheets at least 2 inches apart.
Bake the cookies at 350F for 8-10 minutes until set.
While the cookies are baking, make the frosting by melting the ½ cup butter in a large saucepan over medium heat.
Add the 3 tablespoons milk and 2 tablespoons unsweetened cocoa powder and whisk until smooth.
Add in the powdered sugar and whisk until fully incorporated.