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Make the parfait a week ahead and the sauces a few hours before serving. Chill the butterscotch sauce, but keep the chocolate sauce at room temperature. Note: this recipe contains raw egg.
For the parfait, pour the milk into a medium saucepan and heat gently. Meanwhile, whisk the egg yolks with the sugar in a large bowl, until pale and creamy. When the milk comes to the boil, pour it on to the egg yolks, whisking all the time. Pour the mixture into a clean pan and stir over a low heat until it has thickened enough to coat the back of a spoon. Be careful not to overheat the mixture; allow to cool.
In a bowl, whip the cream to soft peaks. In a separate bowl, whip the egg whites with clean beaters until they form soft peaks, too. Mix the peanut butter into the egg yolk mixture, then gently fold in the whipped cream followed by the egg whites. When thoroughly combined, transfer the parfait to a suitable container, cover and freeze for at least 6 hours.
Peel and slice the banana thinly on the diagonal. Sprinkle with icing sugar and place on a tray lined with nonstick baking paper and then freeze. For the chocolate sauce, heat the cream in a pan then add the chocolate and stir until melted and smooth. Allow to cool to room temperature.
For the butterscotch sauce, heat the sugar in a large pan with 2 tablespoons of water to help it to dissolve. Once it has come to the boil, lower the heat and gently cook the sugar for about 10 minutes, swirling the pan frequently so it cooks evenly, until it caramelises. Then, immediately, but cautiously as it may bubble and spit, add the cream. Bring back to a simmer and whisk until the mixture is smooth.
Allow the sauce to cool for about 10 minutes then whisk in the butter and add a pinch of salt to balance the sweetness. Transfer the sauce to a bowl and leave to cool, then cover and chill for a couple of hours so it thickens.
To serve, remove the parfait from the freezer and let it soften for 10 minutes. Let the banana slices soften for a few minutes, too. Divide the butterscotch sauce between 6 serving glasses. Place a few small scoops of the parfait on top in each glass. Add the banana slices and drizzle with the chocolate sauce.