Preheat the oven to 350 degrees and line a baking sheet with parchment paper. Whisk the flour, cocoa powder, baking soda, and salt in a bowl.
In a second bowl, beat the softened butter and granulated sugar until light. Add the egg, buttermilk, green food coloring, and vanilla extract, then mix until smooth.
Stir the dry ingredients into the wet mixture until just combined. Drop rounded tablespoons of batter onto the baking sheet, spacing them apart, and bake for 10 to 12 minutes.
Cool the cookies completely on a wire rack. While they cool, beat the cream cheese, softened butter, powdered sugar, and vanilla extract until creamy.
Spread the filling on the flat side of half the cookies. Top each with a second cookie to form a sandwich. Press candy eyes onto the tops.