Heat 600ml single cream in a large saucepan over medium until small bubbles begin to form around the edges. Remove from heat and set aside.
Mix the egg yolks and sugar in a large bowl until smooth. While stirring, slowly pour the single cream into the egg mixture. Transfer the mixture back to the saucepan and heat again over medium heat until bubbles begin to form around the edges. Remove from heat and return to the bowl. Stir in the double cream.
Purée the bananas and 175ml cream in a blender until smooth. Add purée to bowl and combine well with cream and egg mixture. Cover and refrigerate until cold, 3 to 4 hours.
Pour mixture into the ice cream maker. (Refrigerate any remaining mixture until ready to freeze.) Freeze according to the manufacturer's directions. Stir in the walnuts.
Transfer to 1 litre containers and freeze overnight before serving.
For added flavour, lightly toast the walnuts before adding to the ice cream.