01 - Preheat the oven to 350°F. Line two baking sheets with parchment paper.
02 - In a large bowl, use an electric mixer to beat the butter and granulated sugar together until smooth and creamy, about 3 to 4 minutes.
03 - Add the vanilla extract and egg to the creamed mixture. Beat until fully combined and smooth.
04 - Mix in the flour, cocoa powder, baking soda, and salt until a dough forms. The dough should come together easily and may be tacky but not overly sticky.
05 - Divide the dough into 16 even portions and roll each into a 1 3/4-inch diameter ball. Arrange on prepared baking sheets. Bake for 8 to 10 minutes, until centers are slightly glossy and edges are set.
06 - Allow cookies to cool on the pan for 10 minutes, then transfer to a wire rack and let cool completely.
07 - In a medium bowl, beat together powdered sugar, unsalted butter, milk, mint extract, and green food coloring if using. Adjust consistency by adding extra powdered sugar to thicken or a splash of milk to thin if necessary.
08 - Evenly spread mint frosting over the tops of the cooled cookies. Place the cookies in the freezer for at least 15 minutes to set the icing before topping with ganache.
09 - Combine the semisweet chocolate and neutral oil in a microwave-safe bowl. Heat in the microwave in 30–40 second intervals, stirring after each, just until fully melted and smooth.
10 - Spoon the ganache over the chilled, frosted cookies. Serve immediately or allow cookies to come to room temperature; chocolate will remain firm.