Gather all ingredients.

Combine half-and-half, both sugars, and salt in a saucepan over medium-low heat; cook and stir until sugars are dissolved, about 5 minutes.

Remove from the heat and transfer 1/2 of the hot mixture to a large bowl. Add eggs to the bowl and whisk until well combined.

Pour mixture back into the saucepan. Stir in cream.

Cook and stir over medium-low heat until mixture is thickened and coats the back of a spoon, 5 to 10 minutes. Remove from the heat and stir in vanilla.

Pour cream mixture over a fine mesh sieve into a bowl; cool to room temperature.

Stir mashed bananas into cooled cream mixture, then pour into an ice maker and freeze according to manufacturer's instructions.

Fold crushed wafers into ice cream during the last 5 to 10 minutes of freezing.