Preheat oven to 350°F.

Whisk together flour, cocoa powder, and espresso powder in a small bowl and set aside. In a large bowl beat the butter with an electric mixer on medium to high speed for about 30 seconds, or until softened. Add sugar, salt, baking powder, and baking soda. Beat until well combined. Add egg and vanilla. Beat well. Gradually beat in the flour mixture.

Shape dough into 1" balls and place on an ungreased baking sheet. Press down on the dough ball with the bottom side of a glass until dough is almost a 2" wide circle. In a small saucepan over medium-low heat, combine chocolate chips and sweetened condensed milk. Heat, stirring regularly, until chocolate is melted and smooth. Briskly stir in mint extract. Turn heat to very low. Spoon a scant teaspoon of the chocolate frosting over the center of each dough round. If the chocolate frosting starts to thicken in the saucepan, whisk briskly to loosen.

Bake about 10 minutes, taking care to not over bake. Remove to wire rack to cool completely.

In the bowl of a stand mixer fitted with a paddle attachment, whip butter on medium-high speed until very fluffy, about 8 minutes, occasionally scraping down the sides and bottom of the bowl. Add powdered sugar and beat on low to incorporate.

Add half and half and mint extract, mixing on low until combined. Increase mixer speed to medium-high and beat until very light and fluffy, about 5 to 6 minutes, occasionally scraping down the sides and bottom of the bowl.

Add green food coloring, if desired, and mix until incorporated.

With a rubber spatula, fold in 2 ounces of the chopped or shaved chocolate.

Using a small scoop or spoon, mound buttercream onto the top of each cookie, aiming to leave the outer edges of the fudge showing. Sprinkle with remaining 1/2 ounce of chocolate shavings.