In a saucepan heat half and half to 175 degrees F. Add in sugar and salt and stir until dissolved.
Spoon a small amount of hot milk mixture into eggs and beat.
Put egg mixture back into pan with rest of milk and whisk together
Cook and stir over low heat until mixture reaches 160 degrees F. Should coat the back of a spoon.
Remove from heat and place pan into a large bowl filled with ice water. Stir to cool.
Add in whipping cream, milk and vanilla.
Cover with plastic wrap and refrigerate for a few hours or overnight.
Add in mashed bananas and place in ice cream maker. Churn according to directions. Refrigerate until ready to serve.