Preheat the oven to 350℉. Brush rolls with melted butter on all sides and place on a baking sheet. Bake in the preheated oven until lightly browned and toasted, 5 minutes. Transfer to a wire rack, so they don't get soggy.
In a mixing bowl, vigorously whisk together the pudding mix, 1½ cups cold milk, vanilla, and salt until well combined and thickened. Fold in whipped topping. Refrigerate for 10 minutes to set up; transfer filling to a piping bag or a plastic bag. (Make a small cut in the corner if using a plastic bag.)
Use a paring knife to make a small cut into one side of each roll, creating an opening large enough to pipe filling into without going all the way through. Fill each hole with about 1 to 1 1⁄2 tablespoons filling.
Heat remaining ¼ cup milk in the microwave, until it's steaming but not boiling, 30 to 40 seconds. Place chocolate chips in a shallow bowl, and pour in hot milk. Let stand 10 seconds; stir until smooth. (If necessary, heat in the microwave 15 seconds to finish melting the chocolate.)
Line a tray with parchment. Dip the top of each filled roll in the melted chocolate, let any excess drip off; place on the tray to cool completely and for chocolate to harden slightly, about 20 minutes, or refrigerate for 5 to 10 minutes before serving.
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Notes
Replace the Cool Whip with an equal amount of homemade whipped cream, if preferred. Beat ¾ cup cold heavy whipping cream with 2 tablespoons powdered sugar to make 1 1⁄2 cups of whipped cream.You will have extra pudding leftover. Enjoy it as is or with some fresh berries!