Place 1 (3.4-ounce) package instant vanilla pudding and 1 1/2 cups cold whole milk in a large bowl and whisk until smooth. Add 3/4 cup creamy peanut butter and whisk until no streaks remain. Add 1 (8-ounce) container thawed frozen whipped topping and fold with a flexible spatula just until combined.

Arrange about 1 sleeve graham crackers in a single, tight layer in the bottom of a 9×13-inch baking pan (about 2 inches high), breaking the crackers as needed to fit. Spread half of the pudding mixture (about 2 1/2 cups) evenly over the graham crackers. Arrange a second layer of graham crackers on top of the pudding mixture. Spread the remaining pudding mixture over the top. Finish with a third layer of graham crackers. You might not have enough graham crackers to completely cover the top, but space them as evenly as possible.

Place 1 cup dark chocolate chips, 3/4 cup heavy cream, 1/4 cup light corn syrup, and 1/8 teaspoon kosher salt in a medium microwave-safe bowl. Microwave on HIGH in 15-second increments, whisking after each increment, until the chocolate is melted and the mixture is completely smooth, about 1 minute total. (Alternatively, heat in a small saucepan on the stovetop over low heat.)

Pour the chocolate mixture evenly over the top layer of graham crackers. Smooth it out with the spatula. Cover and refrigerate for at least 8 hours or up to overnight.