**1. Prepare the Filling:**
- In a large mixing bowl, whisk together the instant pudding mix and cold milk until thickened (about 2 minutes). Gently fold in the whipped topping until fully combined and creamy.
**2. Assemble the Layers:**
- Place a single layer of graham crackers on the bottom of a 9x13-inch baking dish. Spread half of the pudding mixture evenly over the crackers.
- Add another layer of graham crackers, followed by the remaining pudding mixture. Top with a final layer of graham crackers.
**3. Make the Chocolate Glaze:**
- In a medium bowl, whisk together cocoa powder, powdered sugar, milk, melted butter, and vanilla extract until smooth and glossy.
**4. Top the Cake:**
- Pour the chocolate glaze over the top layer of graham crackers, spreading it evenly with an offset spatula or spoon.
**5. Chill:**
- Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight, to allow the graham crackers to soften and the flavors to meld.
**6. Serve:**
- Slice into squares and serve chilled.