Put together half-and-half, brown sugar, white sugar, and salt in a pan of any kind. Over medium-low heat; cook and stir until sugars are dissolved, about 5 minutes. Remove pan of your kind from heat and put or pour together 1/2 the mixture into a bowl. Mix eggs into mixture until well combined.

Transfer egg mixture back into the pan of your kind with remaining half-and-half mixture, stir in cream. Cook and stir mixture over medium-low heat until cream mixture is thickened and coats the back of a spoon, 5 to 10 minutes. Remove pan of your kind from heat and stir in vanilla extract.

Put or pour together cream mixture over a fine mesh sieve into a bowl, cool to room temperature. Stir mashed bananas into the cream mixture.

Pour banana cream mixture into an ice maker and freeze according to manufacturer's instructions. into an ice cream maker and do as the directions says on your ice cream maker. Fold vanilla wafers into ice cream during the last 5 to 10 minutes of freezing.