Place milk, 1 cup of cream, sugar, and salt in a medium sauce pan. Heat until the mixture is steaming, but not boiling. Remove from heat.
Add yolks to a medium bowl and very slowly whisk in warm milk. Transfer mixture back to saucepan and set over medium heat. Stir constantly until mixture thickens slightly and is 170 degrees. Remove from heat immediately so the mixture doesn't scramble.
Place remaining heavy cream in a large bowl and place strainer over bowl. Pour thickened yolk mixture through strainer to remove lumps. Stir with cream. Add vanilla extract. Cover with plastic wrap. Chill mixture until completely cold, about 4-6 hours. In the meantime, make your bananas foster mix.
Add butter to a large skillet. Once melted, add sugar, cinnamon, and 3 tablespoons of maple syrup. Stir to combine. Bring to a simmer and simmer for 1 minute. Add diced bananas and stir together to combine with sugar mixture. Cook bananas for 3 minutes or until soft. Finished by adding half and half. Using a potato masher, mash the bananas into smaller pieces. If the mixture is too thick, add another tablespoons of maple syrup. The mixture should be thick but still thin enough to slide off a spoon. Cover and refrigerate.
Once the vanilla ice cream base is chilled, ice cream base is ready for your machine. Freeze ice cream according to machine instructions.
Once mixture is frozen, place half of ice cream in a storage container. Spoon half of the bananas foster mixture over the ice cream. Swirl the layers together Repeat layer of ice cream and the bananas foster mixture. Cover and freeze ice cream until solid, about 8 hours.