In a bowl, mix cornflour in two tablespoons water. Set aside. Heat milk in a deep non-stick pan. When it comes to a boil, add cornflour mixture and two tablespoons sugar.
Stir to mix and simmer for three to four minutes. Remove from heat and strain. Cool the mixture completely. In another bowl, whip cream with the remaining sugar till soft peaks form.
Add cooled milk mixture, strawberry puree and mashed banana. Mix well. Pour into a shallow dish and freeze in the refrigerator till slushy.
Remove and blend till mixture is smooth and creamy. Freeze again until firm. Scoop and serve.