First, mash your bananas in a bowl until they’re pretty smooth. A few small lumps are fine and will actually add nice texture to your ice cream.
In a large bowl, whisk together the vanilla pudding mix and whole milk until completely smooth, about 2 minutes. You’ll see it start to thicken up – let it sit for about 5 minutes until it’s set to a soft pudding consistency.
While the pudding sets, take about half of your vanilla wafers and crush them into coarse crumbs. Set these aside.
Pour the sweetened condensed milk into your pudding mixture and stir until well combined. Add the mashed bananas and vanilla extract, mixing until everything’s evenly distributed.
In a separate bowl, whip the heavy cream until stiff peaks form – when you lift the beaters, the peaks should stand up straight and not flop over. This usually takes 3-4 minutes on medium-high speed. You want it really well whipped because this is what makes your ice cream light and creamy.
Gently fold the whipped cream into your banana-pudding mixture. I do this in three batches, using a rubber spatula and a light hand. You want to keep as much air in there as possible, but make sure there are no streaks of white cream left.
Pour half of this mixture into a 9×13 freezer-safe container. Sprinkle half of your crushed cookies over the top, then repeat with the remaining ice cream mixture and cookies. Using a butter knife, gently swirl everything together with a few figure-8 motions.
Cover with plastic wrap, pressing it right against the surface of the ice cream to prevent ice crystals from forming. Then cover with a lid or foil.
Freeze for at least 6 hours, but preferably overnight. The ice cream is ready when it’s firm but still scoopable – if it gets too hard, let it sit on the counter for about 5 minutes before scooping.