Preheat oven to 350°F (175°C). Grease a 9x13-inch baking pan.
Prepare the chocolate cake according to package instructions. Pour the batter into the prepared pan and bake as directed, usually about 25–30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool for about 10 minutes. Using the handle of a wooden spoon, poke holes all over the cake about an inch apart.
In a medium bowl, whisk together instant pudding mix and cold milk until slightly thickened (about 1–2 minutes).
Pour the pudding mixture evenly over the cake, spreading it so it fills all the holes. Sprinkle 1 ½ cups chocolate chips over the top while the cake is still warm.
Let the cake cool completely to room temperature, then spread the whipped topping evenly over the surface.
If desired, garnish with mini chocolate chips and drizzle with chocolate syrup before serving.
Refrigerate for at least 2 hours before slicing for best texture.