In a large mixing bowl, whisk together heavy whipping cream, sweetened condensed milk, instant vanilla pudding mix, and vanilla extract until well combined. Pour the mixture into an ice cream maker and churn for about 20-25 minutes, or until the mixture is thick and creamy.
While the ice cream is churning, slice your bananas and crush the vanilla wafers into small pieces using a your hands, rolling pin or food processor. Once the ice cream is done churning, fold in the bananas and crushed vanilla wafers until evenly distributed.
Transfer the ice cream to a freezer-safe container, cover, and freeze for at least 6 hours, or overnight.
To serve, scoop the banana pudding ice cream into bowls and garnish with additional crushed vanilla wafers, if desired.