In a medium saucepan, combine 2 cups of half-and-half, ½ cup light brown sugar, ¼ cup white sugar, and a pinch of salt. Heat over medium-low, stirring gently for about 5 minutes until sugars dissolve. Avoid boiling.

In a separate bowl, whisk together 4 large eggs. Gradually add half of the warm half-and-half mixture, whisking constantly to temper them. Pour back into the saucepan.

Return the saucepan to heat and stir in 1 cup of heavy whipping cream. Cook gently for 5 to 10 minutes until the custard thickens and coats the back of a spoon.

Remove from heat, stir in 1 tablespoon of vanilla extract, and strain through a fine-mesh sieve into a clean bowl to remove cooked egg bits. Let cool.

Mash 2-3 ripe bananas with a fork until smooth and stir into the cooled custard until evenly mixed.

Pour the banana-infused custard into an ice cream maker and churn according to manufacturer's instructions for 20-30 minutes.

In the last 5-10 minutes of churning, fold in 1 cup of crushed vanilla wafers gently.

Transfer the churned ice cream into a lidded container, press plastic wrap against the surface, and freeze for at least 2-3 hours until firm.