In a large bowl, use an electric mixer to beat butter, brown sugar, and vanilla until light and fluffy. Mix in graham crackers, salt, and milk, then fold in chocolate chips. Crumble and pour 1/3 of the mixture into the bottom of a trifle dish.
Make the whipped cream layer: Mix chocolate chips and Cool Whip. Pour 1/3 of the mixture on top of the cookie dough in the trifle dish. Top whipped cream layer with a layer of chocolate chip cookies.
Make chocolate pudding layer: Combine pudding mix and milk, whisking until granules have dissolved. Let pudding set, 5 minutes, then pour 1/3 of the mixture on top of the cookies, smoothing to create an even layer.
Repeat layers until you've reached the top of the dish.
Cover the entire trifle with remaining whipped cream. Refrigerate at least 2 hours, to soften the cookie layers. Top with chocolate chips and crumbled cookie pieces before serving.