In a large saucepan, combine milk, sugar, and salt over medium heat. Stir until sugar is fully dissolved.

In a separate bowl, beat the eggs until smooth. Slowly whisk in a bit of the hot milk mixture to temper the eggs.

Pour the tempered egg mixture back into the saucepan with the rest of the milk. Cook over medium heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon.

Remove from heat and let cool slightly. Stir in the heavy cream and vanilla extract until fully combined.

Add the mashed bananas to the custard mixture and mix until smooth.

Transfer the mixture to a container, cover, and chill in the refrigerator for at least 4 hours or overnight.

Once fully chilled, pour the mixture into an ice cream maker and churn according to manufacturer’s instructions.

When thick and creamy, transfer the ice cream to a freezer-safe container and freeze until firm before serving.