In a medium bowl, whip the heavy cream, powdered sugar, and vanilla extract together until soft peaks form. Be careful not to overwhip.
In serving glasses or bowls, layer the chocolate babka cubes at the bottom.
Add a layer of chocolate pudding over the babka cubes, spreading it evenly.
Spoon a layer of the whipped cream mixture on top of the pudding.
Repeat the layers until the glasses are filled, finishing with a layer of whipped cream on top.
Sprinkle mini chocolate chips and chopped nuts (if using) over the whipped cream layer.
Garnish with fresh berries if desired.
Chill the parfaits in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.