Whisk sweetened condensed milk, regular milk, and dry instant vanilla pudding until well combined. Chill for 5 minutes.
After the pudding has chilled, gently fold in whipped topping. Place the filling in the refrigerator to chill while the waffles cool.
Assemble cake by placing a waffle on a plate and topping it with pudding mixture. Spread the filling evenly. Repeat the process.