Preheat oven to 375°F. Line a baking sheet with parchment paper or lightly grease and set aside.
In a medium bowl whisk together 1 1/4 cups all purpose flour, 1/2 cup unsweetened baking cocoa, 3.9 oz instant chocolate pudding mix (1 box), 1/2 tsp baking soda, and 1/2 tsp salt. Set dry mixture aside.
In a large bowl, beat 3/4 cup light brown sugar and 1/2 cup granulated sugar with 1/2 cup unsalted butter (melted) until combined and slightly fluffy.
Add 1 egg (room temperature), 1 tsp vanilla extract, and 2 tbsp water to the butter-sugar mixture and beat until well blended.
Gradually stir the dry ingredient mixture into the wet ingredients until just combined.
Fold in 1/2 cup semi-sweet chocolate chips and 3/4 cup Andes creme de menthe baking chips.
Using rounded tablespoons of dough, form each portion into a ball. Press one Andes mint into the center of each dough ball (there are 24 mints in the ingredient list; use one per cookie). Fold the dough around the mint so it is enclosed and slightly flatten each cookie. Place cookies on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 8 minutes, or until the cookies are set but not overbaked. Remove from oven and transfer cookies to a wire rack to cool completely.
Melt the remaining 1/2 cup Andes creme de menthe baking chips in a small microwave-safe bowl at 50% power in 30-second intervals, stirring between intervals, until smooth. Transfer the melted chips to a small plastic bag, snip a very small corner, and drizzle over the cooled cookies. Allow this drizzle to set.
Melt 4 oz white candy coating according to package directions. Stir in 1/2 tsp mint extract and green gel food coloring to tint as desired. Transfer the colored coating to a piping bag or plastic bag, snip a corner, and drizzle over the cookies.
Let all drizzles set up completely before storing cookies in an airtight container.