PREHEAT the oven to 350°F (175°C) and line a baking sheet with parchment paper. (See note #1.)
MELT the butter in the microwave in a microwave-safe container. Heat for about 45 seconds. Cool for 2 to 3 minutes.
POUR the dry cake mix and instant pudding mix into a large bowl. Add the melted butter and eggs. Mix with a wooden spoon until the dough is combined. Use a spatula to scrape the sides of the bowl to make sure all the dry ingredients are combined into the cookie dough.
ADD the chocolate chips and stir until combined.
REST the cookie dough for 10 minutes. The moisture will absorb into the dry ingredients leaving the dough the perfect scooping texture. (See note #2.)
SCOOP the cookie dough balls with a large cookie scoop (2 tablespoons size is ideal). Roll the dough ball in your hands to make it smooth. Then flatten the cookie slightly with your palms.
PLACE the cookie dough about two inches apart on the lined baking sheet.
BAKE in the oven for 11 to 13 minutes or until the edges are done. The middles may not look completely done, but they will finish baking with the residual heat when they are out of the oven.
REMOVE the cookie sheet from the oven.
SHAPE the cookies with a large, round cookie ring (optional). Circle the warm cookie with the cookie cutter. Gently spin the ring around the cookie, rotating for about 5 seconds. As the cookie circles, the sides will pull in, and the cookie will get rounder. Repeat this technique with all the cookies.
PLACE the cookie sheet on a wire rack and cool for 5 minutes.
TRANSFER the cookies from the cookie sheet to the cooling rack. Cool them completely.
PLACE the cooled cookies on a sheet of parchment paper.
MELT the chocolate wafers in the microwave. Heat in a microwave-safe bowl at 50% power for 30 seconds. Stir. Repeat heating at 10-second intervals and stirring until the chocolate is melted and smooth. Do not overheat.
TRANSFER the melted chocolate into a pastry bag with a small point. (Or use a zip-top bag with the corner edge snipped off.)
DRIZZLE the melted chocolate back and forth across the cookie.
REST until the chocolate dries.