Using a mixer, cream together butter and sugars on medium-high speed until light and fluffy, about 5 minutes, scrapping the sides of the bowl, as needed. In a separate bowl, whisk flour, cocoa powder, baking soda. Add to wet ingredients and mix on low just until combined.
Using a medium cookie scoop, scoop leveled scoops of dough and place on a large serving platter or plate. Roll the mounds into smooth balls and slightly flatten with your palm. Cover with plastic wrap, and refrigerate for 1 hour, or up to 3 days, before baking. Do not bake with warm dough because cookies will spread and bake thinner and flatter.
Once the dough is chilled, pre-heat oven to 350 degrees. Place dough on cookie sheets lined with parchment paper, about 2 inches apart from one another. Bake for 8 to 9 minutes, rotating cookies halfway through. Do not bake longer than 10 minutes, as they will firm up as they cool.
Allow cookies to cool on the baking sheet for 5 minutes before removing and transferring to a rack to finish cooling.
While the cookies cool, make the butter cream. Add softened butter to a bowl of a stand mixer. Beat on medium low until the butter get fluffy, about 2 minutes. Add powdered sugar, mint extract, half and half and salt. Mix on low until the buttercream comes together. Add 4 drops of green food coloring and mix until icing turns an even mint color. Spread cooled cookies with a layer of mint icing. Place onto a cool baking sheet and into the fridge for 30 minutes.
Add butter and cream to a microwave safe bowl. Microwave for 30 seconds. Place chocolate chips in a bowl. Add hot cream and butter. Let sit for 10 minutes then stir together until smooth. If the chocolate hasn't melted all the way, microwave for another 30 seconds.
Remove cookies from the fridge. Add a dollop of chocolate fudge to the top of each cookie. Let the chocolate set and then serve.