Make the cookie dough

1. Heat the oven to 350°F (175°C). Line two baking sheets with parchment or silicone liners.
2. In a mixing bowl, beat the softened butter and granulated sugar until the mixture becomes smooth and slightly aerated — about 3–4 minutes with an electric mixer.
3. Add the vanilla and the egg, mixing until incorporated.
4. Stir in the flour, cocoa powder, baking soda, and salt until a cohesive dough forms. The dough should hold together; it may feel tacky but shouldn’t be overly sticky.
5. Portion the dough into roughly 16 balls (each about 1¾ inches in diameter). Place them spaced on the prepared sheets.
6. Bake 8–10 minutes, until the edges set and the centers still have a faint sheen. Remove from the oven and let the trays rest for 10 minutes; then transfer cookies to a wire rack to cool completely.

Prepare the mint buttercream

1. In a medium bowl, beat together the powdered sugar and the softened butter. Add the milk, mint extract, and coloring (if using) and whip until light and spreadable.
2. Adjust texture: add a little more powdered sugar to thicken or a splash more milk to loosen.

Assemble and chill

1. Spread or pipe a generous layer of mint frosting onto each cooled cookie. For neat edges, chill the frosted cookies in the freezer for at least 15 minutes — this helps the next step.

Make the chocolate finish

1. Place the chocolate and oil in a microwave-safe bowl. Heat in 30–40 second bursts, stirring between each, until the chocolate melts into a smooth, glossy mixture. (Alternatively, melt over a double boiler on the stovetop.)
2. Spoon the warm chocolate over the frozen frosted cookies so the ganache sets quickly and stays tidy. Let the cookies come to room temperature, or keep chilled if you prefer firmer chocolate.