In a large bowl, whisk the vanilla pudding mix with the cold milk until thick and glossy, about two minutes.
Add the sweetened condensed milk and vanilla extract to the pudding and whisk until completely smooth.
In a separate bowl, whip the heavy cream until soft peaks form.
Gently fold the whipped cream into the pudding mixture until uniform and fluffy.
Slice the bananas into even rounds just before assembling.
Break the vanilla pizzelle cookies into irregular medium pieces by hand.
Spread a thin layer of pudding on the bottom of a trifle dish.
Add a layer of banana slices over the pudding.
Scatter a layer of broken pizzelle cookie pieces over the bananas.
Spoon pudding over the layers, allowing it to settle naturally between gaps.
Repeat the layering process until the dish is filled, finishing with a smooth layer of pudding on top.
Lightly scatter a few small pizzelle crumbs over the top, if desired.
Cover the dish tightly with plastic wrap pressed gently against the surface.
Refrigerate for at least four hours, or overnight, before serving.